If \([x]\) denotes the greatest integer function of \(x\) then \(\int_{a}^{b}[x]dx+\int_{b}^{a}[-x]dx=\)
Answer & explanation
Correct answer: option 1
\(\begin{aligned}\int_{a}^{b}[x]dx+\int_{b}^{a}[-x]dx&=[x]_{a}^{b}+[-x]_{b}^{a}\\ &=2(b-a)\end{aligned}\)