Generalisations of the compound trapezoidal rule

A set of symmetric equidistant quadrature rules with equal internal weights are developed. Some of the rules use the first (and second) derivative(s) in addition to the function values of the integrand. A single unifying concept based on finite element techniques is used to develop this set of quadrature rules. With focus on the quadratures rules' degree of precision we compute the quadrature weights and error estimates for all rules given.