In this paper, we prove that the RSu integral of constant interval-valued functions does not exist according to the definition of [6], and we give a generalized definition of RSu integral of interval-valued functions and fuzzy-valued functions and the integrability of constant interval-valued functions in the sense of new definition. The generalized RSu integral keeps the properties of [6] and especially, we obtain the linearity of integral which also improves the corresponding result in the sense of [6].