Also, how the corresponding Neumann series to this equation help obtain a convergence condition for a general integral equation like $$x(t)-\mu\int_a^bk(t,\xi) x(\xi) d\xi=v(t).$$
I think the second part of this problem is asking us to show $|\mu| < 1/(c(b-a))$. I don't even know how to begin to answer this, I have never even taken a proper course on integral equations.