consider the function $f(x)$, which is defined as \begin{cases} 1,& -1\le x<0, \\ 1/2, &\quad x=0, \\ x,& \phantom{-}0<x\le 1. \end{cases}
This seemed a bit weird to me because of the value it takes at $x=0$, as it is not possible to find the Fourier coefficients for a single point, unless I am much mistaken. Do the sines and cosines just not contribute to the series for $x=0$ as they do with constant functions or is it just not possible to find the Fourier series for the function?