In the present study, we establish some generalized integral formulas involving product of multi-index Bessel function and other polynomials, which are expressed in terms of the Fox-Wright function. Further, ongiving suitable special values to the coefficient in the main results give many known classical polynomials. Therefore, we observe that our main results can lead to yield numerous other interesting integrals involving various Bessel functions and some known polynomials by suitable specialization of arbitrary parameters in the main theorems.