I am trying to find the integral of f(z) = z^2 + 2z + 3 over the curve that is the shorter part of the ellipse x^2 + 4*y = 4 from i to 2.

I figured out that a parameterized form is x = -2cos(t), y=sin(t) for the curve (-2 because of the direction in the complex plan).

But using the formula to solve the integral will create a very complex integral that will take a lot of time to solve, and I feel there is a simpler way. Any suggestions?