Does forgetting to wash one’s feet in ablution invalidate the prayer?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

Scholars unanimously agree that valid ablution is a condition for the prayer’s validity as the Prophet, sallallaahu ‘alayhi wa sallam, said, “Allaah Does not Accept the prayer of anyone of you if he broke his ablution until he performs ablution again.” [Al-Bukhari]

Scholars group acts of ablution into cornerstones, obligations and acts of the Sunnah. 

The cornerstones of ablution include intention, washing the face, washing the hands up to and with the elbows, wiping over the head, washing the feet up to and with the anklebones, keeping the order of these acts, and the immediacy of successiveness. If one left all or any of these cornerstones deliberately or unintentionally and then performed prayer, then his prayer is invalid and he has to perform both ablution and prayer again when he remembers this.

On the other hand, leaving the obligatory acts of ablution unintentionally and leaving acts of the Sunnah deliberately or intentionally, does not invalidate ablution or prayer.

Consequently, the questioner should know that his prayer without washing his feet is invalid, because, in such a case, his ablution is invalid.