If [ ] denotes the greatest integer function then the integral ∫π0[cosx]dx is equal to :

We know that for cosx ∈ [0, π/2] ⇒ 1 ≥ cosx ≥ 0 and cosx ∈ [π/2, π] ⇒ 0 ≥ cosx ≥ -1
∫π0[cosx]dx = ∫π/20 0 dx + ∫ππ/2 -1 dx = -π/2