Question: sin integral when m::even, solving the Laplace equation in rectangular coord

I have this very simple intergral

((Int(sin(m*Pi*y/a), y = 0 .. b))

I want to solve it when m is even then when it is odd. Of course, a and b are real positive. Then I will do the same with the other side of the integral.

Int(sin(n*Pi*y/a)*sin(m*Pi*y/a), y = 0 .. b)

Thank you in advance.


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