In this paper, we establish new integral formulas whose integrands involve the function \(_{p}R_{q}(\alpha ,\beta ;z)\) , with the resulting expressions represented in terms of generalized M-series. The main results are derived by employing a known definite integral due to Lavoie and Trottier, leading to unified representations that connect generalized hypergeometric functions with Mittag-Leffler-type functions. The obtained results have potential applications in fractional calculus, integral transforms, and in the solutions of differential and integral equations arising in mathematical physics and engineering sciences. Furthermore, several explicit special cases are presented, including those involving generalized hypergeometric functions, Mittag-Leffler functions, and related special functions, thereby demonstrating the applicability and effectiveness of the derived formulas.
