Calculate the double integrals:

I)

IntInt R (x-y^2)dA

where R is the region bounded by the curves y = x^2 and y = x^3

II)

IntInt D x^3 sin(y^3)dydx

where D is the region bounded by the parabola y = x^2 and the two straight lines x = 0 and y = 1

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I will be forever grateful for all the help I can get.