It is well aware that integral inequalities provide a very handy and effective tool to the study of differential and integral equations. Among various types of integral inequalities, the Gronwall-Bellman type is particularly useful, as they provide explicit bounds for the unknown function. We will give some new Gronwall-Bellman type inequalities which on the one hand generalize the existing results in the literature and on the other hand provide qualitative as well as quantitative properties of the solutions to certain boundary value problems.