Does this day count as a make-up day after one forgets the intention to fast, and eats and drinks, then abstains for the rest of the day?

Whoever eats or drinks forgetfully while fasting, his fast is valid and there is no expiation required of him, for the Prophet, peace and blessings be upon him, said: "Whoever forgets while he is fasting and eats or drinks, let him complete his fast, for it was Allah who fed him and gave him drink." There is no difference in this regard between the fast of Ramadan (definition), or a make-up fast, or a vowed fast, or a voluntary fast.