Will someone help me on this problem?

Let $\displaystyle f(x):R \rightarrow R$ be a continuous but differentiable nowhere ( for example the Weierstrass's function). Define $\displaystyle F(x)=\int_0^x f(r)dr$. Why does F(x) has the first derivative everywhere?

Does F(x) have a second derivative?

I think F(x) has the first derivative since that's why the FTOC part 2 says, but I'm stuck on part 2.