Let $f$ be a real valued continuous function on $\left[0, 1\right]$ and $f\left(x\right)=x+{\int }_0^1\left(x-t\right)f\left(t\right)dt$. Then which of the following points $\left(x, y\right)$ lies on the curve $y=f\left(x\right)$?

• A

  $\left(2, 4\right)$
• B

  $\left(1, 2\right)$
• C

  $\left(4, 17\right)$
• Correct answer
  D

  $\left(6, 8\right)$

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