Abstract
The aim of the present paper is to evaluate new finite integral formulas involving polynomials and Ī-function. The values of the formulas are obtained in terms of ψ(z) (The logarithmic derivative of Γ(z)). These integral formulas are unified in nature and act as key formula from which we can obtain as their special cases. For the sake of illustration we record here some special cases of our main formulas which are also new and known. The formulas establish here are basic in nature and are likely to find useful applications in the field of science and engineering.