Primary 26D10, Secondary 41A55.

In the article ''N. Ujevic, A generalization of the pre-Grüss inequality and applications to some quadrature formulae, J. Inequal. Pure Appl. Math., 3(2), Art. 13, 2002'' error bounds for some quadrature formulae are established. Here we prove that all inequalities (error bounds) obtained in this article are sharp. We also establish a new sharp averaged midpoint-trapezoid inequality and give applications in numerical integration.