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Question

Let f:[0,2]R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1.
Let F(x)=x20f(t)dt, for xϵ[0,2], If F(x)=f(x),xϵ(0,2), then F(2) equals

A
e21
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C
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D
e4
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