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If f'(x) = f(x)+ int (0)^(1)f (x) dx and...

If `f'(x) = f(x)+ int _(0)^(1)f (x)` dx and given `f (0) =1,` then `int f (x) dx` is equal to :

A

`(2e^(x))/(3-e)+(1-e)/(3-e)`

B

`(e^(x))/(3-e) +(1+e)/(1-e)`

C

`(3e^(x))/(2-e)+(1+e)/(1-e)`

D

`(3e^(x))/(2-e)+(1-e)/(3+e)`

Text Solution

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The correct Answer is:
A
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