The value of the definite integral ∫a+2πa+5π/2 sin−1⁡(cos⁡x)+cos−1⁡(sin⁡x)dx is equal to

∵sin−1⁡(cos⁡x)+cos−1⁡(sin⁡x) is periodic with period  2π then∫a+2πa+5π/2 sin−1⁡(cos⁡x)+cos−1⁡(sin⁡x)dx=∫0π/2 sin−1⁡(cos⁡x)+cos−1⁡(sin⁡x)dx=∫0π/2 sin−1⁡cos⁡π2−x+cos−1⁡sin⁡π2−xdx=∫0π/2 sin−1⁡sin⁡x+cos−1⁡cos⁡xdx=2∫0π/2 xdx=2x220π2=π24