Let $\mathbb{R}$ be the set of all real numbers and $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x)=\int_0^1|x-t| d t$. The number of times the graph of $g(x)=f(x)-x$ cuts the $x$-axis between the lines $x=0$ and $x=1$ is

• A

  $0$
• Correct answer
  B

  $1$
• C

  $2$
• D

  $3$

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