For \(0\leq x\leq \pi\), the area bounded by \(y=x\) and \(y=x+\sin x\) is

\(2\) \(4\) \(2\pi\) \(4\pi\)

\(4\)

\(\text{Area}=2\left[\int_{0}^{\pi}(x+\sin x)dx-\int_{0}^{\pi}xdx\right]\)