I am studying complex analysis and I saw integral like this $$ y = \int_{-\infty}^\infty \frac{s\cdot \mathrm{exp}(ist)}{s^2-z^2}ds. $$ And this integral has clearly two poles $s=z$ and $s=-z$. I know how to calculate this using residue theorem, but in every source they claim that for $s>0$, we h...