\begin{array}{l}
 \int {(1 - \frac{c}{d}x)^2 dx}  = \left| \begin{array}{l}
 1 - \frac{c}{d}x = t \\ 
  - \frac{c}{d}dx = dt \\ 
 dx =  - \frac{d}{c}dt \\ 
 \end{array} \right| =  - \frac{d}{c}\int {t^2 dt}  =  - \frac{d}{c}\frac{{t^3 }}{3} =  - \frac{d}{c}\frac{{(1 - \frac{c}{d}x)^3 }}{3} \\ 
 \int\limits_b^a {(1 - \frac{c}{d}x)^2 dx}  =  - \frac{d}{c}\frac{{(1 - \frac{c}{d}x)^3 }}{3}\left| {_b ^a } \right. =  - \frac{d}{{3c}}\left[ {(1 - \frac{c}{d}a)^3  - (1 - \frac{c}{d}b)^3 } \right] \\ 
 \end{array}