So, I want to integrate $\int_\gamma sinz\; dz$ where $\gamma$ is any curve joining $i\to \pi$. Can I say that it is beacause $\int sinz=-cosz$, and $-cosz$ is analytic on the domain containing $\gamma$, so I just need to take the difference between endpoint and initial point?
So, I will have $\int_\gamma sinz\; dz=-cos(\pi)+cos(i)=1$?
Did I do that right?