In this paper, we will improve and generalize inequality of Ostrowski type for mappings whose second derivatives belong to L1 (a, b). Some well known inequalities can be derived as special cases. In addition, perturbed mid-point inequality and perturbed trapezoid inequality are also obtained. The obtained inequalities have immediate applications in numerical integration where new estimates are obtained for the remainder term of the trapezoid and midpoint formula. Applications to some special means are also investigated. © 2015 Academic Publications, Ltd.