  We consider optimal approximation with respect to the mean square error of
It\^o integrals and Skorohod integrals given an equidistant discretization of
the Brownian motion. We obtain for suitable integrands optimal rates smaller
than the standard $n^{-1}$, where $n$ denotes the number of evaluations of the
Brownian motion. For the It\^o integral this is due to the Weyl
equidistribution theorem and discontinuities of the integrand. For the Skorohod
integral the situation is more complicated and relies on a reformulation of the
Wiener chaos expansion. Here, we specify conditions on the integrands to obtain
optimal rates $n^{-1/2}$, respectively, examples of lower rates.
