Can someone help me numerically integrate some integrals involving quotient and $\sin(x)$?

Question

I am trying to numerically integrate the following integrals ($*$ is multiplication symbol):

(1) $$ \dfrac{1}{4}\dfrac{\sin(\pi y) - \sin(\pi x)}{y - x}*\dfrac{(\sin(\pi x)*y - \sin(\pi y)*x)}{y - x}$$

over $x \in [-1, 1], y \in [-1, 1]$

I tried to punching this integral into Wolframalpha, but I received a time out error

and

(2) $$\dfrac{1}{4}\dfrac{\sin(\pi x)*y - \sin(\pi y)*x}{y - x}$$

over $x \in [-1, 1], y \in [-1, 1]$

I also tried punching this into Wolframalpha but I also received a time out error

Can someone please help me integrating these functions? I am certain that they are supposed to have solutions.

Answer 1

Both integrals are $0$, by the symmetry $x\to -x$, $y \to -y$.

If you insist on doing it numerically, Maple can do it:

evalf(Int(1/4*(sin(Pi * y)-sin(Pi * x))/(y-x) * (sin(Pi * x) * y - sin(Pi * y) * x)/(y-x),[x=-1..1,y=-1..1]));

$$ 0.$$

evalf(Int((sin(Pi * x) * y-sin(Pi * y) * x)/(x-y),[x=-1..1,y=-1..1]));

$$ 0. $$