In this paper, first we evaluate a finite integral involving general class of polynomials and the product of two H -functions and then we make its application to solve boundary value problem on heat conduction in a rod under the certain conditions and further we establish an expansion formula involving about product of H -function. In view of generality of the polynomials and products of H -function occurring here in, on specializing the coefficients of polynomials and parameters of the H -function, our results would readily reduce to a large number of results involving known class of polynomials and simpler functions.