Summary: We discuss the numerical improvement of the open Newton-Cotes integration rules that 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 the integral bounds are considered as two additional variables (i.e. and in fact) we reach a nonlinear system that numerically improves the precision degree of the above integration formula up to degree . In this way, some numerical tests are given to show the numerical superiority of our idea with respect to the usual open Newton-Cotes integration rules.