Hi there!

Let

be a rectifiable, smooth enough curve. Then we have:

You parametrisation is correct, try also applying to it the Euler formula.

Find out about the Cauchy-Riemann differential equations (if you think you'll need a differentiation of the integrand function).

For the integral, check out when a holomorphic function has an antiderivative and most importantly - WHERE.

When you're ready, compare your resuld with the Cauchy's integral formula.