In the present paper, we obtain three new finite integral formulas. These formulas involve the product of a general class of polynomials and the generalized Meliin- Barnes type of contour integrals. Mainly we are using series representation of the H-function given by Agarwal [14], Agarwal and Jain [13]. These integral formulas are unified in nature and act as the key formulas from which we can obtain as their special cases. By giving suitable values to the parameters, our main integral formulas are reduces to the Fox H-function, the G-function and generalized wright hypergeometric function.