Where the story is told
The story is in Surah al-Ma'idah, in Quran 5:27-32. Allah tells the Prophet ﷺ to recite to the people the story of the two sons of Adam "in truth", which means as it really happened, without exaggeration.
The Quran does not give the names of the two sons. The names Habil (Abel) and Qabil (Cain) are well known from tradition and commentaries, but they are not in the Quran or in the authentic hadith used here. This page therefore says "the two sons of Adam" and uses the names only for easy recognition.