Numerical resolution of ian ntegral equation

I have to solve the following:
f(x)=a + b*Sum[m]*Int[y;f(y)K(m,x,y)] +
c*Sum[m]*Int[y,z;f(y)f(z)K(m,x,y,z)]
where f(x) is 2pi-periodic, the sum goes [-m,m] and th integrals
[-pi,pi].
I have tried an iterative method with Simpson one third rule for
integration, but the result I get look somewhat wrong. I'd like to know
if somebody as a better method.

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