$ \frac {1}{2\pi i} \int \frac {(e^z)}{z-\pi i} dz$, around a rectangle with vertices at: $(a)$ $2 \pm i$,$ -2 \pm i$ $(b)$ $-i, 2 - i, 2 + i, i.$

Question

How to calculate $$ \frac {1}{2\pi i} \int \frac {(e^z)}{z-\pi i} dz,$$ around a rectangle with vertices at: $(a)$ $2 \pm i$, $-2 \pm i$ $(b)$ $-i, 2 - i, 2 + i, i.$

I want to solve this math by Cauchy integral formula. $b$ answer is $\frac{-1}{2}$. I can't find this