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 \({\int }_{-\pi /2}^{\pi /2}[[x]-\sin x]dx\) is equal to:

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