[m]f(c)=\frac{ ∫_{\frac{π}{6}}^{\frac{π}{4}}sinxdx }{\frac{π}{4}-\frac{π}{6}}=\frac{(-cosx)|_{\frac{π}{6}}^{\frac{π}{4}}}{\frac{π}{12}}=\frac{-cos\frac{π}{4}+cos\frac{π}{6}}{\frac{π}{12}}=\frac{-\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{2}}{\frac{π}{12}}=\frac{6(\sqrt{3}-\sqrt{2})}{π}[/m]