Error bounds in approximating the Riemann-Stieltjes integral of Cn+1-class integrands and nonsmooth integrators

In the present paper we investigate the problem of approximating the Riemann-Stieltjes integral ∫abf(λ)du(λ) in the case when the integrand f is (n+1)-time differentiable (n⩾0) and the derivative f(n+1) is continuous on [a,b], while the integrator u is Riemann integrable on [a,b]. A priory error bounds for different classes of functions are provided.