# Real analysis

${{\lim_{\substack{x\rightarrow\pi}} {\left( \frac {x}{x-\pi}{\int_{\pi}^{x} }\frac{sin t}{t}} dt\right)}$
Of course, you can treat the "x" outside the integral separately- it goes to $\pi$. That leaves $\frac{\int_\pi^x\frac{sin(t)}{t}dt}{x- \pi}$ which is of the form "0/0". Use L'Hopital's rule for that.