  We analyze univariate oscillatory integrals for the standard Sobolev spaces
$H^s$ of periodic and non-periodic functions with an arbitrary integer $s\ge1$.
We find matching lower and upper bounds on the minimal worst case error of
algorithms that use $n$ function or derivative values. We also find sharp
bounds on the information complexity which is the minimal $n$ for which the
absolute or normalized error is at most $\varepsilon$. We show surprising
relations between the information complexity and the oscillatory weight. We
also briefly consider the case of $s=\infty$.
