Please see the attached file for the fully formatted problems.
I = integration (along C) [x*y*dx + x^2*y^3*dy]
By Green's theorem,
integration(along C)[f1*dx + f2*dy]
= integration (over region E) [ del(f2)/del(x) - del(f1)/del(y)]dx*dy
f1 = x*y => del(f1)/del(y) = x,
f2 = x^2*y^3 => ...
Green's Theorem is used to evlauate a line integral. The solution is well-explained.