A note to Ujević's generalization of Ostrowski's inequality

Following the main ideas of X.H. Wang [Remarks on some quadrature formulas, Math. Numer. Sin. 3 (1978) 76-84 (in Chinese)], we give a unified treatment of error estimates for a general quadrature rule satisfying a natural condition with integrand or its derivatives being of bounded variation or absolutely continuous. We also generalize theorems concerning Ostrowski's inequality in N. Ujević [A generalization of Ostrowski's inequality and applications in numerical integration, Appl. Math. Lett. 17 (2004) 133-137] with the differentiability conditions weakened.