If $[\cdot]$ denotes the greatest integer function, then $\int_1^2\left[x^2\right] d x=$

• A

  $5+\sqrt{2}+\sqrt{3}$
• B

  $5+\sqrt{2}-\sqrt{3}$
• Correct answer
  C

  $5-\sqrt{2}-\sqrt{3}$
• D

  $5-\sqrt{2}+\sqrt{3}$

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