Does a Muslim receive reward for intentions he forgot or was unaware of in acts of worship, despite their confirmation in authentic hadiths, or is the reward limited only to what he intended and remembered?

If a person is keen to obtain the full reward for an act of obedience, but forgets or is ignorant of some of that reward, he will receive the full reward — by Allah's permission. This is a manifestation of Allah's vast mercy and grace. A Muslim should strive to gain a deep understanding of his religion, for the more he comprehends, the greater his reward and goodness will be in the sight of Allah. The Prophet, peace and blessings be upon him, said: "When Allah desires good for someone, He gives him understanding in the religion."