Uniformly convergent Fourier serie

Question

In my book it says that if F (of causeF'=f) is continuous and piecewise differentiable and if F'=f for all non-break-points then is the Fourier serie for F uniformly convergent. But do F have to be piecewise differentiable and not just differentiable?. Do $F(x)=e^{-x}$, $x\in(-\pi,\pi$) and $F(-\pi)=F(\pi)=\frac{1}{2}(e^{\pi}+e^{-\pi})$ for example have an uniformly convergent Fourier serie on $x\in[-\pi,\pi]$?