URGENT please help:ellipse

Using Green's formula, evaluate the integral

C(x+y)-dx(x-y) dy, where

C is the ellipse

x^2/a^2+b^2+a^2=1

i no the area of an ellipse is piab but i must show this is the case in relation to the question im not sure how thsi is done!!!i no using greens formula for that integral that its -2 thus the final answer will be 2piab

howvere i have started by using jacobian to obtain abdudvwith th ellipse being u^2+v^2=1 howvere im unsure of whatlimits to put into the above integral abdudv to get pi can anyone help please it would be much appreciated!!!! thanks