Could someone help me through this problem?
This theorem is already proved: Suppose f is entire and D is the boundary of a rectangle R. Then $\displaystyle\int_{D} f(z)\, dz$
Now he must prove this directly from the theorem: given any rectangle with vertices (a, c), (b, c), (b, d) and (a, d), parameterize the boundary D and verify directly that $\displaystyle\int_{D}\, dz=$$\displaystyle\int_{D}z\, dz=0$