Let $f$ be a continuous function on $[0,1]$ and $F$ be its antiderivative. If $F(0)=1$ and $\int_0^1 f(x) d x=1$, then $F(1)$ is

• Correct answer
  A

  $2$
• B

  $\frac{1}{2}$
• C

  $1$
• D

  $0$

Hence, the correct answer is option: 'A'.