Hadith: Whoever forgets that he is fasting and eats or drinks, let him complete his fast, for it was Allah who fed him and gave him to drink

عن أبي هريرة رضي الله عنه عن النبي صلى الله عليه وسلم قال: «مَنْ نَسِيَ وَهُوَ صَائِمٌ فأَكل أو شَرِب، فَلْيُتِمَّ صَوْمَهُ، فَإِنَّمَا أَطْعَمَهُ الله وَسَقَاهُ».
[صحيح] - [متفق عليه]

Abu Hurayrah (may Allah be pleased with him) reported that the Prophet (may Allah's peace and blessings be upon him) said: "Whoever forgets that he is fasting and eats or drinks, let him complete his fast, for it was Allah who fed him and gave him to drink."
Sahih/Authentic. - [Al-Bukhari and Muslim]

Explanation

The Islamic Shariah is built upon ease and facilitation, and on assigning people with obligations that are within their capacity to fulfill, as well as overlooking what is beyond the ability or choice. This is clear in this Hadīth that states that whoever forgetfully eats or drinks or commits another act that breaks the fast during the daytime of Ramadan, or while fasting on any other day, then he should complete his fast for the fast is still sound because he had no choice. Whatever one does out of forgetfulness, without intention, it does not affect the validity of his fast; rather, it is from Allah who made him eat and drink.