Questions & Answers about Kynlíf er hluti af lífinu.
Because the preposition af requires the dative case in Icelandic.
Here are the relevant forms of líf (life):
- líf = nominative/accusative, indefinite
- lífið = nominative/accusative, definite
- lífi = dative, indefinite
- lífinu = dative, definite
Since the sentence says af lífinu (of life / of the life), the noun after af must be in the dative, so lífinu is the correct form.
This is a very common learner question. Icelandic and English do not use the definite article in exactly the same way.
In English, we say part of life.
In Icelandic, the natural phrase is hluti af lífinu, literally part of the life.
That does not mean Icelandic is talking about one specific life in a narrow sense. It is just the idiomatic, natural way to express the idea. So it is best not to translate the article mechanically word-for-word here.