Obećavam da neću varati.

Obećavam is the 1st person singular present tense of the verb obećavati/obećati: I promise.

In this sentence, Obećavam means I am promising / I promise.

Why not obećam? Because:

• obećavam is the normal present-tense form used for I promise
• obećam can exist as a form of the perfective verb obećati, but perfective present forms in Serbian often refer to a future-like completed action or appear in specific contexts, not usually as the ordinary neutral I promise here

So for a straightforward promise, Obećavam is the natural choice.

In Serbian, da often introduces a subordinate clause, especially after verbs like:

• obećavati / obećati = to promise
• misliti = to think/intend
• želeti = to want
• nadati se = to hope

So Obećavam da... literally means something like:

• I promise that...

In English, we can say both:

• I promise I won’t cheat
• I promise that I won’t cheat

Serbian generally uses da here.

Neću is the normal Serbian way to say I will not.

It is the negative form of hoću (I will / I want):

• hoću = I will
• neću = I will not

So:

• neću varati = I will not cheat

This is how Serbian forms the future in many common sentences:

• ja ću raditi = I will work
• ja neću raditi = I will not work

So in your sentence:

• Obećavam da neću varati = I promise that I will not cheat

Because in standard Serbian, the negative forms of hteti / hoću are written together:

• neću
• nećeš
• neće
• nećemo
• nećete
• neće

This is something learners just have to remember.

Compare:

• hoću = I will
• neću = I will not

So ne ću is not standard spelling.

Because after the future auxiliary ću / ćeš / će / ćemo / ćete / će and its negative forms like neću, Serbian commonly uses the infinitive.

Examples:

• Ja ću doći = I will come
• Neću spavati = I will not sleep
• Neću varati = I will not cheat

So the structure is:

• neću + infinitive

That is why you get:

• neću varati

and not a present-tense form like varam.

Yes, many speakers would also say:

• Obećavam da neću da varam

This is also natural in many varieties of Serbian.

There are two common patterns:

• neću varati
• neću da varam

Both can mean I won’t cheat.

Very roughly:

• neću + infinitive is often felt as a bit more neutral or standard in careful written language
• neću da + present tense is also very common in speech

So your original sentence is completely correct, but learners should know the alternative exists.

Here varati means to cheat.

Depending on context, varati can also mean:

• to deceive
• to trick
• to be unfaithful / cheat on someone

So the exact English meaning depends on context.

For example:

• Varam na testu. = I cheat on a test.
• Vara me. = He/She is deceiving me. / He/She is cheating on me.

In Obećavam da neću varati, the likely meaning is simply I promise I won’t cheat, but Serbian itself leaves the exact context open.

This is a question of aspect, which is very important in Serbian.

• varati = imperfective
• prevariti = usually perfective

Very roughly:

• imperfective focuses on the action as ongoing, repeated, or general
• perfective focuses on a completed whole action

In promises like this, Serbian often prefers the imperfective when talking about not engaging in a type of behavior:

• neću varati = I won’t cheat

That sounds like I won’t do that / I won’t be cheating as a general promise.

Neću prevariti would usually mean something more like I will not deceive / trick someone once, successfully, as a completed act, and in many contexts it would not fit as well.

So varati is the natural choice for a general promise about behavior.

Because Serbian often drops subject pronouns when the verb ending already shows who the subject is.

Here:

• Obećavam already means I promise
• neću already means I will not

So ja is not necessary.

You could say:

• Ja obećavam da neću varati

but that adds emphasis, something like:

• I promise / I myself promise

In neutral speech, leaving out ja is very normal.

Yes, Serbian word order is fairly flexible, though some versions sound more natural than others.

The neutral order is:

• Obećavam da neću varati.

You may also hear emphasis changes, for example:

• Da neću varati, obećavam.

But that is much less neutral and more stylistically marked.

For learners, the best default is to keep:

• Obećavam da neću varati.

The tricky sound here is ć.

• ć is a soft sound, somewhat like a very soft ty/ch sound
• it is softer than č

So:

• neću sounds roughly like NEH-tyoo or NEH-choo with a very soft middle sound
• obećavam sounds roughly like oh-BEH-tya-vam

Also note:

• ć and č are different letters in Serbian
• learners often mix them up at first

You do not need a perfect English equivalent, but it is important to hear that ć is softer than č.

It is neutral and works in both everyday speech and standard written Serbian.

It is not especially formal, but it is fully correct and natural.

So you could use it:

• in conversation
• in writing
• in a serious promise
• in a casual situation

That makes it a very useful model sentence.