What is \(\mathop \smallint \limits_{\frac{1}{3}}^{\frac{1}{2}} {\rm{g}}\left( {\rm{x}} \right){\rm{dx\;}}\) equal to?

• A. \(\frac{1}{6}\)
• B. \(\frac{1}{3}\)
• C. \(\frac{5}{{18}}\)
• D. \(\frac{5}{{36}}\)