I was asked to compute the fourier series of $f(x)=x$ in two different intervals: $x \in [0,2\pi]$ and $x\in [-\pi,\pi]$. What is the real difference between the two series, cause we know that for periodic functions $\int_{0}^{T}f(x)dx=\int_{a}^{a+T}f(x)dx$, so I don't really get it.
Thank you so much