On some inequalities related to open Newton-Cotes formulas for differentiable convex functions with applications

In this paper, first, we prove a novel integral identity involving a single time-differentiable function. Then, we prove some new inequalities associated with one of the open Newton-Cotes formulas for differentiable convex functions. The newly established inequalities can be helpful in finding the error bounds of one of the open Newton-Cotes formulas. Finally, some applications of the inequalities are also presented in the context of open Newton-Cotes formulas.