Integral of (cos^2 z) from ( - pi ) iota along |z|= pi to (pi) iota in the right half plane
STATE IF THE FUNCTION IS ANALYTIC OR NOT AND THEN INTEGRATE USING PARAMETRIC REPRESENTATION IF NOT ANALYTIC OR SIMPLY INTEGRATE using calculus IF ANALYTIC.

$\int_{-\pi}^{\pi} \cos^2(z) dz$
$=\int_{-\pi}^{\pi} \frac{1+\cos(2z)}{2} dz$
$=\frac{1}{2}z+\frac{1}{4}\sin(2z)$ from -Pi to Pi
$=\frac{\pi}{2} + \frac{\pi}{2} + 0 - 0 = \pi$