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.