1) The document presents theorems for determining the univalence of integral operators of certain forms. Specifically, it obtains conditions for the univalence of operators of the form F(z) and H(z), which involve integrals involving functions g(s) that satisfy certain constraints. 2) It proves Theorem 1, which provides conditions on the parameter λ for which the operator F(z) is univalent, if g(s) satisfies the given constraints. 3) It proves Theorem 2, which provides conditions on the parameters Reλ and Imλ for which the operator H(z) is univalent, if g(s) satisfies the given constraints.