Summary: This paper discusses on numerical improvement of the Newton-Cotes integration rules, which are in forms of:
It is known that the precision degree of above formula is for even ’s and is for odd ’s. However, if its bounds are considered as two additional variables (i.e. and in fact) we reach a nonlinear system that numerically improves the precision degree of above integration formula up to degree . In this way, some numerical examples are given to show the numerical superiority of our approach with respect to usual Newton-Cotes integration formulas.