I got stuck on this problem. Hope anyone could give some help.

Let $\displaystyle f:R \rightarrow R$ be continuous and $\displaystyle \epsilon >0$. Define $\displaystyle g(t)=\int_{t-\epsilon}^{t+\epsilon}f(x)dx$ for all $\displaystyle t \in R$. Show that g is differentiable and find g'