Is it true that fasting Ramadan out of faith and hope for reward atones for previous missed prayers, or is it obligatory to make them up?

Fasting and observing Ramadan, including the Night of Decree (Laylat al-Qadr), out of faith and hope for reward, atones for sins. However, this is conditional upon abstaining from grave sins. Abandoning prayer is one of the grave sins, so it is not forgiven by fasting Ramadan. Moreover, the forgiveness of sins does not nullify duties or the need to make up missed obligations.