A companion of Dragomir's generalization of Ostrowski's inequality and applications in numerical integration - Alomari, M. W. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
\lambda) f(x) - \int^b_a f(t)dt\right]\right| \leq$$$$\leq\left[\frac{(b-a)^2}{4}(\lambda^2 + (1 - \lambda)^2) + \left(x - \frac{a + b}{2}\right)^2\right] ||f'||_{\infty}$$are established. Some sharp inequalities are proved. An application to a composite quadrature rule is provided.