In this paper we study a linear integral equation x(t) = a(t)− ∫ t 0 C(t, s)x(s) ds, its resolvent equation R(t, s) = C(t, s) − ∫ t s C(t, u)R(u, s) du, the variation of parameters formula x(t) = a(t) − ∫ t 0 R(t, s)a(s) ds, and a perturbed equation. The kernel, C(t, s), satisfies classical smoothness and sign conditions assumed in many real-world problems. We study the effects of perturbations of C and also the limit sets of the resolvent. These results lead us to the study of nonlinear perturbations.