\int_0^{\pi/2} arctg(\sin{x})dx-\int_0^{\pi/2} arctg(\cos{x})dx=\int_0^{\pi/4} arctg(\sin{x})dx+\int_{\pi/4}^{\pi/2} arctg(\sin{x})dx-\int_0^{\pi/4} arctg(\cos{x})dx-\int_{\pi/4}^{\pi/2} arctg(\cos{x})dx