Let $f:[0,2 \pi] \rightarrow \mathbb{R}$ be a differentiable, strictly increasing function such that $f(0) \lt 0 \lt f(2 \pi)$. Let $F(t)=\int_0^t f(x) d x$ for all $t$ in $[0,2 \pi]$. Then

• A

  $F$ is an increasing function on $[0,2 \pi]$
• B

  $F$ is a decreasing function on $[0,2 \pi]$
• Correct answer
  C

  $F$ has a minimum in the interval $(0,2 \pi)$
• D

  $F$ has a maximum in the interval $(0,2 \pi)$

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