$$\int_C e^zdz = 0$$
Let C be the perimeter of the square with vertices at the points z = 0, z = 1, z = 1 +i and z = i.
$$z = x + iy$$
The Attempt at a Solution
I know that if a function is analytic/holomorphic on a domain and the contour lies within the domain lies. Then this integral equals 0. I can prove that e^z is analytic everywhere. (using cauchy-riemann) Is that enough to show it works in this case?