Use the Dirac function in an integral calculation?

Questions
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1

Consider the following code:

Integrate[F[t]*DiracDelta[(x - c)*(y - d)]*Sin[(Pi*m*x)/a]*Sin[(Pi*n*y)/b], 
{x, 0, a}, {y, 0, b},  Assumptions -> Element[{a, b, c, d}, Reals]]

I need to do the calculation on, but not the results, Hope everyone help.

2

What result did you get? What is wrong with it?