Answer
$\pi^2$
Work Step by Step
We need to integrate the integral as shown below:
$I=\pi \int_{(\pi/4)}^{(5 \pi/4)} (\sin x -\cos x)^2 dx \\=\pi \int_{(\pi/4)}^{(5 \pi/4)} (1- \sin (2x)) dx \\=\pi [x+\dfrac{\cos (2x) }{2}] _{\pi/4}^{5 \pi/4} \\=\pi^2$
