Let $f:[0,1] \rightarrow[0,1]$ be a non-constant continuous function different from the identity function. Then

• Correct answer
  A

  the graph of $f$ meets the line $y=x$ at least once
• Correct answer
  B

  there exists $x_0 \in[0,1 / 2]$ such that $f\left(x_0\right)=f\left(x_0+1 / 2\right)$ if $f(0)=f(1)$
• C

  the set $\{x \in[0,1]: f(f(x))=x\}$ is empty
• Correct answer
  D

  there exists $y_0 \in[0,1]$ such that $\int_0^{y_0} f(t) d t=\int_{y_0}^1 f(t) d t$

Hence, the correct answer is options: 'A', 'B', 'D'.