Riemann's example of an integrable function with infinite points of discontinuity. Of course, we cannot really draw it but at least we can have an idea of how it looks with a sufficient number of elements of the serie: [math]\sum_{k=1}^{n} \frac{(kx)}{k^2}[/math].[br][br]Click on the Animation bottom.[br][br]The function is defined as follows: [math]f(x)=\sum_{k=1}^{\infty} \frac{(kx)}{k^2}[/math], which is discontinuous on a dense subset of the real numbers. Nevertheless, [math]f[/math] is integrable.