If the integral $I=\int \frac{x\sqrt{x}-3x+3\sqrt{x}-1}{x-2\sqrt{x}+1}dx$$=f\left(x\right)+C$ (where, $x>0$ and $C$ is the constant of integration) and $f\left(1\right)=\frac{-1}{3}$, then the value of $f\left(9\right)$ is equal to

• A

  $3$
• B

  $6$
• Correct answer
  C

  $9$
• D

  $12$

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