Verify whether the following operators $L^2[a, b] \to L^2[a, b]$ are finite-rank operators.
a) $Kf(t) = \sum_{j = 1}^n \phi_j(t)\int_a^b \psi_j(s) f(s)\,\mathrm ds$, where $\phi_j, \psi_j \in L^2[a, b]$;
b) $Mf(t) = \int_a^t \phi(s)\,\mathrm ds$, where $\phi \in L^2[a, b]$.
For the first one we have that $$Kf(t) = \sum_{j = 1}^n \alpha_j \phi_j(t),\qquad \alpha_j \in \mathbb F$$ and therefore $\operatorname{Im} K \subset \operatorname{span}\{\phi_j\}_{j = 1}^n$, giving $$\dim\operatorname{Im}K < n$$ and so the first one is finite-rank.
I have no idea how to approach the second one though, any hints?