Cauchy-Goursat Theorem/Examples/z squared over e to the it

Example of use of Cauchy-Goursat Theorem
Let $\gamma \left({t}\right) = e^{i t}$.

Give $\gamma$ the domain $\left[{0, 2 \pi}\right)$.

Now, let $f \left({z}\right) = z^2$.

Then: