We study the logarithmic error of numerical methods for the
integration of monotone or unimodal positive functions.
We compare adaptive and nonadaptive methods in the worst
case setting. It turns out
that adaption significantly helps for the class
of unimodal functions, but does not help for the class of
monotone functions.
We do not assume any smoothness properties of the integrands and
obtain numerical methods that are reliable even for
discontinuous
integrands. Numerical examples show that our method
is very competitive in the case of nonsmooth and/or peak functions.
Journal of Complexity 12 (1996), 358-379.