Consider integrating sin(t)/t from 0 to infinity via the Taylor expansion method. If you do that then you will get infinite terms in the series which clearly is wrong as that integral equals pi/2. Can anyone tell me why using the Taylor expansion method dosen't work? It always dosen't work when integrating to infinity. But other methods like complex integral does work. Why? Taylor expansion use to be a sure thing for me every time but now my innocence has been broken.