Find the partial fraction decomposition for the following rational expression. $$\frac{8-\left(6t^{2}+7t\right)}{(t+4)(t-1)(t-2)}=\frac{A}{t+4}+\frac{B}{t-1}+\frac{C}{t-2}$$

Answer: $A =$ , $B =$ , and $C =$

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Using the partial fraction decomposition above, evaluate the integral $$\int \frac{8-\left(6t^{2}+7t\right)}{(t+4)(t-1)(t-2)} \,dt.$$ Answer:

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