In the field of Engineering and Applied Mathematical Sciences, minimizing approximation error is very important task and therefore quadrature rules are investigated regularly. In this paper, using some standard results of theoretical inequalities, e.g. Ostrowski type inequality, some new efficient quadrature rules are introduced for n-times differentiable mappings. These quadrature rules are expected to give better results comparing to the conventional quadrature rules. © 2016 Author(s).