With the aid of an errorbound arithmetic (see ), formulas are given for the computation of approximate values plus errorbounds for integrals. In the simplest case, no further information is required about the integrand (e. g. bounds for derivatives, etc.). The formulas can be given for each order of exactitude, the order for the approximate value being, in general, one higher than the order of the errorbounds. Examples show that the errorbounds are generally very sharp. It is possible to use the information given by the errorbounds for the fully automatic ending of the quadrature at the "optimal" point. © 1966 Springer-Verlag.