The value of $\sum_{n=1}^{100} \int_{n-1}^n e^{x-[x]} d x$, where $[x]$ is the greatest integer $\leq x$, is: [JEE Main 2021, 26 Feb (Shift 1)]

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The value of \(\sum_{n=1}^{100} \int_{n-1}^n e^{x-[x]} d x\), where \([x]\) is the greatest integer \(\leq x\), is: [JEE…