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Let the function f:[0,2] to RR be define...

Let the function `f:[0,2] to RR` be defined as
`f(x)={(e^(min{x^2,x-[x]}),x in [0,1)),(e^[[x-log_e x]],x in [1,2]):}` where `[t]` denotes the greatest integer less than or equal to `t`. Then the value of the integral `int_0^1 x f(x) dx` is

A

`(e-1)(e^2+1/2)`

B

`2e-1`

C

`2e-1/2`

D

`1+(3e)/2`

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