A unified generalization of some quadrature rules and error bounds
  By introducing a parameter, we give a unified generalization of some quadrature rules, which not only unify the recent results about error bounds for generalized mid-point, trapezoid and Simpson's rules, but also give some new error bounds for other quadrature rules as special cases. Especially, two sharp error inequalities are derived when n is an odd and an even integer, respectively. 
Wenjun Liu, Yong Jiang and Adnan Tuna
math.NA