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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) = ∫ 2 x 0 dt ) t ( f for x ∈ [0, 2]. If F ′ (x) = f ′ (x) for all x ∈ (0, 2), then F(2) equals

1. e 2 – 1
2. e 4 – 1
3. e – 1
4. e 4

Correct answer: e 4 – 1

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