This paper outlines several ways to evaluate the integral of the product of two \(B\)-spline functions. Integrals of these forms arise in applications such as the finite element method and least squares function fitting when \(B\)-splines are used as basis functions. The splines may be of different orders and defined on different knot sequences. A detailed description of an algorithm that is based on integration by parts is given. The algorithm reduces the integral to a sum of evaluations of a higher-order spline. This reduction involves differentiating one spline by differencing its coefficients, and integrating the other by summing its coefficients.