In this paper, we establish a new inequality of Theorem 2 [Appl. Math. Lett. 13 (2000) 19] (Dragomir's integral inequality) for functions whose derivatives are bounded. This has immediate applications in numerical integration where new estimates are obtained for the remainder term of the trapezoid, mid-point. Some natural applications to special means of real numbers are given. For several recent results concerning Dragomir's integral inequality (see [Appl. Math. Lett. 13 (2000) 191] where further references are listed). (C) 2002 Elsevier Science Inc. All rights reserved.