<p>This article explores the existence and controllability results within the classes of second-order functional integro-differential equations with infinite delay. The study uses a Schauder fixed-point theorem that works in a stochastic domain to show that there are mild solutions to this problem. Additionally, rigorous proofs outlining the controllability of these problems despite the complexities introduced by infinite delay are provided. As an example of how the theory can be used in real life, an example is given to show that the established theory works for dealing with systems with infinite delay in a controlled environment.</p>