_ -2 ¹[x+1] d x= (Where [x] is greatest integer function not greater than x )

Step-by-step solution

aligned _ -2 ¹[x+1] d x &= _ -2 ⁻¹([x]+1) d x+ _ -1 ⁰([x]+1) d y+ ₀¹([x]+1) d x &= _ -2 ⁻¹(-2+1) d x+ _ -1 ⁰(-1+1) d x+ ₀¹(0+1) d x &=-[x]_ -2 ⁻¹+0+[x]₀¹=-(-1+2)+0+(1-0) &=0 aligned