Question: Let \(I=[0,1] \times[0,1]\) and \(P=[0, \pi] \times[0, \pi]\). Evaluate each of the following integrals, using standard techniques from calculus:

1. \(\int_{I} x^{m} y^{n} \mathrm{~d} x \mathrm{~d} y\), where \(m, n>0\);
2. \(\int_{I} \sin (x+y) \mathrm{d} x \mathrm{~d} y\)
3. \(\int_{P} \sin ^{2} x \cos ^{2} y \mathrm{~d} x \mathrm{~d} y\).

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