The aim of this paper is to establish new inequalities which are more generalized than the inequalities of Dragomir, Wang and Cerone. The current article also obtains bounds for the deviation of a function from a combination of integral means over the end intervals covering the entire interval. A variety of earlier results are recaptured as special cases of the inequalities obtained. Some new perturbed results and application for cumulative distribution function are also discussed. © 2016, University of Nis. All rights reserved.