If \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of the integral \(\int_{-\pi / 2}^{\…

If \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of the integral \(\int_{-\pi / 2}^{\pi / 2}[[x]-\sin x] d x\) is equal to:

[JEE Main 2021, 20 Jul (Shift 2)]