Let `f:[0,2]->R` be a function which is continuous on [0,2] and is differentiable on (0,2) with `f(0)=1` `L e t :F(x)=int_0^(x^2)f(sqrt(t))dtforx in [0,2]dotIfF^(prime)(x)=f^(prime)(x)` . for all `x in (0,2),` then `F(2)` equals (a)`e^2-1` (b) `e^4-1` (c)`e-1` (d) `e^4`