In this study, a functional Volterra integral equation of the second kind is investigated. Some conditions are provided which ensure the existence and uniqueness of the solution to this equation in the space of square integrable functions. Then, we derive the operational matrix of integration corresponding to sigmoidal polynomials and utilize it alongside the collocation method to approximate the solution. This approach transforms the considered functional integral equation into a system of nonlinear algebraic equations, which can be solved using conventional numerical methods or iterative methods.
