What is the ruling on the prayer of one who forgot to recite the surah and remembered while bowing in the same rak'ah, so he rose from the bowing position, recited the surah, then completed his prayer, and performed a prostration of forgetfulness thereafter?

Reciting a chapter after Al-Fatihah is recommended, not obligatory, according to the majority of scholars. If one omits it by mistake, he is not permitted to go back and recite it, and the preponderant opinion is that prostration of forgetfulness (sujud (definition) al-sahw) is not required in this case. A worshiper returning to recite the chapter is an error and an addition that invalidates the prayer if done intentionally. However, if he was ignorant of the ruling, his prayer is valid and he does not need to repeat it, for the worshiper's ignorance or forgetfulness does not invalidate the prayer.