  We consider a generalized form of certain integral inequalities given by
Guessab, Schmeisser and Alomari. The trapezoidal, mid point, Simpson,
Newton-Simpson rules are obtained as special cases. Also, inequalities for the
generalized Alomari functional in terms of the $n$-th order modulus,
$n=\overline{1,4}$, are given and applied to some known quadrature rules.
