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Let f:[0,2]to RR be a function which is ...

Let `f:[0,2]to RR` be a function which is continuous on `[0,2]` and is differentiable on (0, 2) with `f(0)=1`.
Let `F(x)=int_(0)^(x^(2))f(sqrt(t))dt" for "x in[0,2]`. If `F'(x)=f'(x)` for all `x in(0,2)`, the F(2) equals

A

`e^(2)-1`

B

`e^(4)-1`

C

`e-1`

D

`e^(4)`

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