Currently there are a number of papers in which certain types of splines are used to solve the Fredholm equation. Now much attention is paid to the application of a new type of spline, the so-called integro-differential spline to the solution of various problems. In this paper we consider the solution of the Fredholm equation using polynomial integro-differential splines of the third order approximation. To calculate the integral in the formula of a quadratic integro-differential spline, we propose the corresponding quadrature formula. The results of numerical experiments are given.