Certain comparisons of Iyengar-Mahajani’s and Kesava Menon’s integral inequalities with Hermite-Hadamard-Jensen’s integral inequalities are considered and some mistakes in the paper [On certain inequalities by Iyengar and Kesava Menon, Octogon Math. Mag. 4 (1996), no. 1, 9–11.] are corrected. Some applications of these inequalities to elementary functions are carried out and several inequalities involving mean values are obtained.