The aim of the present research is to study some new finite integrals. Here, first we obtain six new finite double integrals involving the product of the H-function and Srivastava polynomials. Γhe values of the integral are obtained in terms of а(z) (the logarithmic derivative of Γ(z)). Next for all findings, we establish an interesting integral relation in terms of H-function. Present findings are the most general in nature and act as the key formulas from which we can obtain their special cases. [ABSTRACT FROM AUTHOR]