Let $f(x)$ be a function such that $f^{\prime}\left(\frac{1}{x}\right)+x^3 f^{\prime}(x)=0$, What is $\int_{-1}^1 f(x) d x$ equal to?

• A

  $2 \mathrm{f}(1)$
• B

  $0$
• Correct answer
  C

  $2 \mathrm{f}(-1)$
• D

  $4 \mathrm{f}(1)$

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