Hello, thanks a lot for your answer. You mean to try something like:
i1[k_, f_,q_]=Map[Integrate[#, {b, a, q}] &, eq[k, q, b, f] // FullSimplify // Expand]
i2[k_,q_]=Map[Integrate[#, {f, a, q}] &, i1[k,f,q] // FullSimplify // Expand]
But it takes so much time to be evaluated. Is there a way to speed up the integration ?