Use algebraic division to express \(\frac { x ^ { 3 } - 2 x ^ { 2 } - 4 x + 13 } { x ^ { 2 } - x - 6 }\) in the form \(A x + B + \frac { C x + D } { x ^ { 2 } - x - 6 }\), where \(A , B , C\) and \(D\) are constants.
Hence find \(\int _ { 4 } ^ { 6 } \frac { x ^ { 3 } - 2 x ^ { 2 } - 4 x + 13 } { x ^ { 2 } - x - 6 } \mathrm {~d} x\), giving your answer in the form \(a + \ln b\).