Concept:For x<0, ∣x∣=−x.The integral of a constant c is cx+C.Explanation:We are given I=−2∫−1​∣x∣x​dx.Over the interval [−2,−1], x is negative, so ∣x∣=−x.Thus ∣x∣x​=−xx​=−1.Therefore I=−2∫−1​(−1)dx.Evaluating: I=−[x]−2−1​=−[(−1)−(−2)]=−[−1+2]=−[1]=−1.Answer:−1 (Option B)