Explanation

Use integration by parts:
Let $u=x$, $dv=\cos (x)dx$

Then:

$$\int x\cos (x)dx=x\sin (x)-\int \sin (x)dx=x\sin (x)+\cos (x)$$

Evaluate from $0$ to π/2

$$= left( frac{pi}{2} cdot 1 + cosleft( frac{pi}{2} right) right) - left( 0 + cos(0) right) = frac{pi}{2} - 1$$

π/2​−1