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Integration and integral transforms are playing an important role in various branches of applied mathematics and physical sciences. In the present article, first we define modified I-function of two variables and after that we will set up and prove two double integral formulas involving a product of I-function with two other special functions. In the last, we have given some integral transforms of these two double integral formulas and it is our belief that the results derived in this paper are new in literature. [ABSTRACT FROM AUTHOR]