Compute the following integrals: a. (int_{C}left(x^{2}+y ight) d x+left(3 x+y^{3} ight) d y) for (C) the ellipse

Compute the following integrals:

a. \(\int_{C}\left(x^{2}+y\right) d x+\left(3 x+y^{3}\right) d y\) for \(C\) the ellipse \(x^{2}+4 y^{2}=4\).

b. \(\int_{S}(x-y) d y d z+\left(y^{2}+z^{2}\right) d z d x+\left(y-x^{2}\right) d x d y\) for \(S\) the positively oriented unit sphere.

c. \(\int_{C}(y-z) d x+(3 x+z) d y+(x+2 y) d z\), where \(C\) is the curve of intersection between \(z=4-x^{2}-y^{2}\) and the plane \(x+y+z=0\).

d. \(\int_{C} x^{2} y d x-x y^{2} d y\) for \(C\) a circle of radius 2 centered about the origin.

e. \(\int_{S} x^{2} y d y d z+3 y^{2} d z d x-2 x z^{2} d x d y\), where \(S\) is the surface of the cube \([-1,1] \times[-1,1] \times[-1,1]\).