A sharp estimate for the Peano error representation

We provide a sharp estimate of the Peano error representation formula for linear functionals. As applications, we obtain sharp estimates for the remainder term in general quadrature formulae and expand some Ostrowski-like type inequalities to linear functionals. The new approach extends and unifies many earlier results on the subject (Dragomir and Wang, 1997; Cheng, 2001; Matić, 2003; Vong, 2011; Gonska et al., 2012).