[SOLVED] Line integral, Cauchy's integral formula

Let $\displaystyle C$ be the frontier of the square whose sides are the lines $\displaystyle x=\pm 2$ and $\displaystyle y= \pm 2$. (orientation is positive)

Calculate the following integral using Cauchy's integral formula for a function or its derivative.

$\displaystyle \int _C \frac{e^{-z}dz}{z-\frac{i\pi}{2}}$.

My attempt : I find confusing the "using Cauchy's integral formula for a function or its derivative.", I don't really know what they mean by that.

So Cauchy's formula is $\displaystyle f(z)=\frac{1}{2\pi i} \int _C \frac{f(\xi)}{\xi -z}d \xi$.

Looking at the integrand of the integral, I see that it is not defined for $\displaystyle z=i \frac{\pi}{2}$. Does that mean that $\displaystyle f$ is not analytic in this point?

I believe the integral should equals $\displaystyle 2 \pi i$, I don't really know why.

I need help, I find all this new theory somewhat hard to grasp due to the amount of it.

(Bow)