Is the following statement true or not?

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> If $f$ is Riemann integrable on $[a,b]$, then the function $F(x)=\int\_a^xf(t)dt$ is differentiable on $(a,b)$ and $F'(x)=f(x)$ for $x\in (a,b)$
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I think it is not. Since $F$ is differentiable at the point where $f$ is continuous, but I can not think a counter example, is anyone has a counterexample? Thanks a lot.