I had to calculate the Fourier Series $\left(\displaystyle{\sum_{n=-\infty}^{\infty}}c_n\,e^{i\,n\,t}\right)$ of
$g(t)= \begin{cases}\sinh(t),&-\pi<t<\pi \\\\ 0, &t=\pi\end{cases}$
Just like I did, in the solutions $c_n$ was calculated like $\dfrac{1}{2\,\pi}\displaystyle{\int_{-\pi}^{\pi}g(t)\,e^{-i\,n\,t}}\,\mathrm{dt}$
Why is that possible the reason being $c_n$ actually is discontinuous at $t = \pi$?