Simple question about delta-Dirac function

Question

I can not understand this mathematical formula:

$$\int_{a-\epsilon}^{a+\epsilon}f(x)\delta(x-a)dx=f(a)$$

I understand that it is the derivative of an integral evaluated in $a$, but still can not explain in mathematically.

How do you get $f(a)$ from the integral side? and what are the assumptions you have to do?

Answer 1

I find a great answer here (pags 2-3)