If $[x]$ is the greatest integer $\leq x$, then $\pi^2 \int_0^2\left(\sin \frac{\pi x}{2}\right)(x-[x])^{[x]} d x$ is equal to: [JEE Main 2021, 31 Aug (Shift 2)]

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If \([x]\) is the greatest integer \(\leq x\), then \(\pi^2 \int_0^2\left(\sin \frac{\pi x}{2}\right)(x-[x])^{[x]} d x\)…

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