If $\int x^3 \sin 3 x d x=\frac{1}{27}[f(x) \cos 3 x+g(x) \sin 3 x]+\mathrm{c}$ then $f(1)+g(1)=$

• A

  $14$
• B

  $6$
• Correct answer
  C

  $4$
• D

  $12$

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