Learn French: J'ai oublié de peindre le capot.

In French, many verbs require a specific preposition before a following infinitive. The verb oublier (to forget) always takes the preposition de when followed by an action (an infinitive verb). Whenever you say 'I forgot to do something,' the structure is oublier de followed by the infinitive.

If I wanted to say I forgot a physical object instead of an action, would I still use de?

No. If you forget a noun (a thing or a person), you connect it directly without de. For example, 'I forgot the hood' would simply be J'ai oublié le capot. The de here acts purely as a grammatical bridge connecting oublier to the next verb.

What kind of verb is peindre, and are there others like it?

Peindre (to paint) is an irregular -re verb that ends in -eindre. Other verbs with this ending, like éteindre (to turn off) or atteindre (to reach), follow the exact same irregular conjugation pattern.

Why doesn't the past participle oublié have any extra agreement letters at the end?