Residue theorem to solve improper integrals

Question

This is an example of using the residue theorem to solve improper integrals. My question is how the πi term came about, because my understanding is $\int_{C{_R}}1/z dz=2 πi$ and not πi. Sorry I must be missing something simple here

Answer 1

$\Gamma_R$ is surely a semi-circle, so we just pick up $i\pi$.

Answer 2

Note that

$$\begin{align} \int_{\Gamma_R}\frac1z\,dz&=\int_0^\pi \frac{1}{Re^{i\phi}}\,iRe^{i\phi}\,d\phi\\\\ &=\pi i \end{align}$$