Is it narrated in the Sunnah of the Prophet (peace and blessings be upon him) that he would raise his hands and supplicate upon rising from rukoo’ (bowing), and what is the correct action if that is a mistake?

The Sunnah (definition) is for the worshiper, after rising from bowing (ruku'), to say: "Our Lord, to You be praise, filling the heavens and the earth, and filling whatever else You wish thereafter. Worthy of praise and glory, the truest thing a servant has said, and we are all Your servants. O Allah, there is none to withhold what You give, and none to give what You withhold. And the might of the mighty does not benefit them against You." Some scholars are of the view that prolonging this pillar (standing after ruku') for a duration equal to reciting Al-Fatiha invalidates the prayer, while others do not hold this view. As for raising the hands in the manner of supplication (du'a'), it is not prescribed except in the case of Qunut.