Let a function $f:\left[0,5\right]\to R$ be continuous, $f\left(1\right)=3$ and $F$ be defined as:
$F\left(x\right)={\int }_1^x{t}^{2}g\left(t\right)dt,$ where $g\left(t\right)={\int }_1^{t}f\left(u\right)du.$

Then for the function $F\left(x\right),$ the point $x=1$ is:

• Correct answer
  A

  a point of local minima
• B

  not a critical point
• C

  a point of local maxima
• D

  a point of inflection

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