If [x] denotes the greatest integer less than or equal to x, then the value of the integral ∫(x - sin x) dx, x ∈ [-π/2,π/2] is equal to : (1) – π

Question

If [x] denotes the greatest integer less than or equal to x, then the value of the integral

\(\int \limits_{π/2}^{-π/2}\)(x - sin x)dx is equal to : 

(1) – π

(2) π

(3) 0

(4) 1

Answer 1

Answer is: (1) – π

(King property)