SubArea: Definite integralLevel: BProject ID: 1003118904Source Problem: 2010001202Accepted: 1Clonable: 1Evaluate the definite integral. \[ \int\limits_{-\frac{\pi}2}^{\pi}x\cdot\sin x\,\mathrm{d}x \]\( \pi+1 \)\( \pi-1 \)\( \frac{\pi+2}2 \)\( \frac{\pi}2 \)