The value of $\int_0^{1000}e^{x-[x]}dx$ is ([.] denotes the greatest integer function):

1000e 1000(e - 1) 1001(e - 1) None of these

1000(e - 1)

$I=\int\limits_0^{1000}e^{\{x\}}dx=1000\int\limits_0^{1}e^{\{x\}}dx=1000(e-1)$