The second kind Chebyshev-Newton-Cotes quadrature rule (open type) and its numerical improvement

The precision degree of the above formula is n + 1 for even n's and is n for odd n's but if one considers its upper and lower bounds as two additional variables, a nonlinear system will be derived whose solution improves the precision degree of above formula up to degree n + 2 numerically. In this way, some examples are given to show the numerical superiority of our idea.