I am studying the famous integral of $\dfrac{\sin x}{x}$ in complex analysis. My lecturer integrated $e^{iz}/z$ over a semi-circle with $0$ (the origin), taken out by a small semi-circle.
He asked us to think about why he chose $e^{iz}/z$ and not $e^{-iz}/z$.
My guess is it is something to do with wanting the contour to be traversed anti-clockwise and not clockwise. Is this along the right lines?