In this paper, we will improve and generalize Ostrowski type inequality for twice differentiable mappings in terms of the upper and lower bounds of the second derivative. Some well known inequalities can be derived as special cases of the inequalities obtained here. In addition, perturbed mid-point inequality and perturbed trapezoid inequality are also obtained. The obtained inequalities have immediate applications in numerical integrations where new estimates are obtained for the remainder term of the trapezoid and midpoint formulae. Applications to special means are also investigated. © 2014 Ather Qayyum, Muhammad Shoaib and Muhammad Amer Latif.