Let $ \gamma$ be a Jordan curve and denote by $S$ the area on the inside of this curve. Prove that
$$\int_\gamma x\,dz = -i\int_\gamma y \, dz = \frac 1 2 \int_\gamma \bar{z} \, dz = iS$$
how am i suposed to parametrize this Jordan curve in terms of $x$ and $y$ to integrate?