  Some selected Ostrowski type inequalities and a connection with numerical
integration are studied in this survey paper, which is dedicated to the memory
of Professor D.S. Mitrinovic, who left us 25 years ago. His significant
influence to the development of the theory of inequalities is briefly given in
the first section of this paper. Beside some basic facts on quadrature formulas
and an approach for estimating the error term using Ostrowski type inequalities
and Peano kernel techniques, we give several examples of selected quadrature
formulas and the corresponding inequalities, including the basic Ostrowski's
inequality (1938), inequality of Milovanovic and Pecaric (1976) and its
modifications, inequality of Dragomir, Cerone and Roumeliotis (2000), symmetric
inequality of Guessab and Schmeisser (2002) and asymmetric inequality of
Franjic (2009), as well as four point symmetric inequalites by Alomari (2012)
and a variant with double internal nodes given by Liu and Park (2017).
