complex analysis - Prove that $lim_{R rightarrow infty} int_{sigma_1}f(z) dz=0$.

Let $$f(z)=\frac{e^{\pi iz}}{z^2-2z+2}$$
and $\gamma_R$ is the closed contour made up by the semi-circular contour $\sigma_1$ given by, $\sigma_1(t)=Re^{it}$, and the straight line $\gamma_2$ from $-R$ to $R$ (so the contour of $\gamma_R$ appears to be a semi circle).

Prove that $$\lim_{R \rightarrow \infty} \int_{\sigma_1}f(z) dz=0.$$