This and your last question contained fairly easy integrals. If you are having trouble with them, please make sure try to point out what it is so we can help you.

In my (rather ugly) notation, we have:

Int[ Int[(1 - 6x^2*y) dy, -1, 1] dx, 0, 2]

vs.

Int[ Int[(1 - 6x^2*y) dx, 0, 2] dy, -1, 1]

The first is:

Int[ Int[(1 - 6x^2*y) dy, -1, 1] dx, 0, 2]

= Int[ [y - 3x^2*y^2, -1, 1], dx, 0, 2]

= Int[2 dx, 0, 2] = [2x, 0, 2] = 4

The second is:

Int[ Int[(1 - 6x^2*y) dx, 0, 2] dy, -1, 1]

= Int[ [x - 2x^3*y, 0 , 2] dy, -1, 1]

= Int[(2 - 16y) dy, -1, 1]

= [2y - 8y^2, -1, 1] = 4

-Dan