Chọn phương án B.

\(\begin{aligned}
\displaystyle\int\limits_{3}^{5}\dfrac{\mathrm{d}x}{x^2-x}&=\displaystyle\int\limits_{3}^{5}\dfrac{1}{x(x-1)}\mathrm{\,d}x\\
&=\displaystyle\int\limits_{3}^{5}\dfrac{x-(x-1)}{x(x-1)}\mathrm{\,d}x\\
&=\displaystyle\int\limits_{3}^{5}\left(\dfrac{1}{x-1}-\dfrac{1}{x}\right)\mathrm{\,d}x\\
&=\left(\ln|x-1|-\ln|x|\right)\bigg|_3^5\\
&=-\ln5+\ln3+\ln2.
\end{aligned}\)

Theo đó, \(a=-1\), \(b=1\), \(c=1\).

Suy ra \(S=-2\cdot(-1)+1+3\cdot1^2=6\).