In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value theorem", Int. J. Math. Ed. Sci. Tech. 38(6) (2007), pp. 818-822]. The importance of our results are illustrated by interesting examples.