Is my fast broken if I eat by mistake?

If you genuinely eat, drink or have intercourse while you are fasting, out of forgetfulness, your fast is not broken.

Abu Hurayrah (may Allah be pleased with him) narrated that the Prophet (peace be on him) said:

“Whoever forgets he is fasting and eats or drinks, let him complete his fast for it is Allah Who has fed him and given him to drink.” (Bukhari and Muslim)

You do not have give expiation or make up that fast. 

 In the Quran, in Surat al Ahzab, it says:

And there is no sin on you if you make a mistake therein, except in regard to what your hearts deliberately intend. And Allah is Ever Oft-Forgiving, Most Merciful. (33:5)

Shaykh Haytham Tamim