Show that $$\lim_{n\to \infty}\int_0^{10}\frac{n[11-x]}{1+n^2x^2}dx=11\frac{\pi}{2}$$ $[x]$ denotes the greatest integer function
here $[11-x]$ is discontinuous at $0,1,2,..,10$ so i divide this integration and after solve i don't get this answer. Thank you for your help.