I had an exam a few days ago and one of the questions in it was to decide if f(x) defined below, admits an improper integral in I = ($-\infty,\infty$). I have no idea how to show that f has or hasn't an improper integral on I.
\begin{equation} f(x)=\left\lbrace \begin{array}{ll} (sin(1/x))^2 & \mbox{if $ x \neq 0$} | \pi /2 & \mbox{if $ x = 0$} \end{array} \right\rbrace. \end{equation}