If f is Riemann integrable and continuous, prove that F is differentiable

Some help on this following question, please. Thanks a bunch!

Question: If $\displaystyle f$ is Riemann integrable on $\displaystyle [a,b]$ and continuous at $\displaystyle x_0$, prove that $\displaystyle F(x) = \int_{a}^{x} f(t) dt$ is differentiable at $\displaystyle x_0$ and $\displaystyle F'(x_0)=f(x_0)$. Show that if $\displaystyle f$ has a jump discontinuity at $\displaystyle x_0$, then $\displaystyle F$ is not differentiable at $\displaystyle x_0$.