Let $f(x)=\sin \pi x$ and $g(x)=x-[x]$, where $[x]$ is the largest integer not exceeding $x$. Then

• A

  $g(x) \lt f(x)$ for all $x \in(0,1)$.
• Correct answer
  B

  $\int_0^1 g(x) \mathrm{d} x \lt \int_0^1 f(x) \mathrm{d} x$.
• C

  $\lim _{x \rightarrow 1^{+}} \frac{f(x)}{g(x)}=-1$
• Correct answer
  D

  there exists a unique point $x_0 \in(0,1)$ such that $f\left(x_0\right)=g\left(x_0\right)$.

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