O you who have believed, decreed upon you is fasting as it was decreed upon those before you that you may become righteous.
(Surah Al-Baqarah 2:183)
Narrated Abu Hurairah (may Allaah be pleased with him):

Allah's Messenger (pbuh) said, "Whoever observes fasts during the month of Ramadan out of sincere faith, and hoping to attain Allah's rewards, then all his past sins will be forgiven."
(Sahih Bukhari 38)