The aim of this paper is to evaluate four finite integrals involving the product of Srivastava's polynomials, a generalized hypergeometric function and ${ar H}$-function proposed by Inayat Hussian which contains a certain class of Feynman integrals. At the end, we give an application of our main findings by connecting them with the Riemann-Liouville type of fractional integral operator. The results obtained by us are basic in nature and are likely to find useful applications in several fields notably electric networks, probability theory and statistical mechanics.

Keywords: ${ar H }$ -function, generalized hypergeometric function, general class of polynomials, freactional integral operators