LaTeX Forum

\documentclass[11pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}

\begin{document}
  \begin{align*}
    \sideset{}{^\ast}\int_a^b f(x)\,dx \\
    \sideset{}{_\ast}\int_a^b f(x)\,dx
  \end{align*}
\end{document}

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
\int\limits_a^{b*}f(x)dx \\
{\int\limits_a^b}^*f(x)dx \\
\int\limits_a^b{}^*f(x)dx\\
\end{align*}
\end{document}

\documentclass{scrartcl}

\usepackage{selinput}
\SelectInputMappings{
  adieresis={ä},
  germandbls={ß},
  Euro={€}
}
\usepackage{amsmath}

\begin{document}

$\int\limits_a^b{}^*f(x)dx$

$\int\limits_a^b{}_*f(x)dx$

\end{document}