Is it valid for one to fast to make up for a missed fast if he intended to fast at night, then forgot and ate, drank, and had intercourse during the day, and remembered before sunset, so he abstained?

The intention for making up missed fasts (qada') must be set from the night before. Your fast is valid, Allah willing, and being forgetful in doing things that break the fast does not harm it. This is because the preponderant opinion is that whoever eats or drinks while fasting out of forgetfulness, their fast remains valid, whether it was a little or a lot, as long as they did not intentionally do anything that breaks the fast. This is the view of the majority of scholars. Therefore, you are not required to make up that day, nor is expiation (kaffarah (definition)) required, as it is only obligatory for intentionally breaking a fast in Ramadan (definition).