Let π : E → X and ρ : F → X be bundles of Banach spaces, where X is a compact Hausdorff space, and let V be a Banach space. Let Γ ( π ) denote the space of sections of the bundle π . We obtain two representations of integral operators T : Γ ( π ) → V in terms of measures. The first generalizes a recent result of P. Saab, the second generalizes a theorem of Grothendieck. We also study integral operators T : Γ ( π ) → Γ ( ρ ) which are C ( X ) -linear.