Explanation

(b)
Let $I = \int_{5}^{10}{\frac{1}{(x - 1)(x - 2)}dx}$
$\int_{5}^{10}\left\lbrack \frac{- 1}{x - 1} + \frac{1}{x - 2} \right\rbrack dx$
$= \left\lbrack - \log(x - 1) + \log(x - 2) \right\rbrack_{5}^{10}$
$= - \log{9 + \log{8 + \log{4 - \log 3}}}$
$= - 2\log{3 + 3\log{2 + 2\log{2 - \log 3}}}$
$= - 3\log{3 + 5\log 2}$
$= - \log{27 + \log 32}$
$= \log\frac{32}{27}$