Let G = (V (G), E(G)) be an undirected connected graph and let X be a subset of V (G) . Furthermore, let I (X ) and B(X ) denote the set of isolates and the boundary set of X, respectively. The inner boundary number of X, denoted by (X ) i is (X) = max{|Y |:Y X and B(X Y) Y = B(X)}. i   The outer boundary number of X, denoted by (X ) o  is (X ) =|V(G) N[X ]| . o  The I -integral of X is I  (X ) = (X ) (X ) | I(X ) | i o     and the I -integral of G is I  (G) = min{ I  (X ) : X V(G)}I . In this paper, we determine the I -integral of graphs resulting from some binary operations such as the join, corona, composition, and cartesian product of graphs.