I having trouble using partial fractions. For the integral below I have to use partial fractions, however I am at a lost on how to do so.
$$\int\frac{dt}{t^2-t-20}$$

The farthest I have gotten to is factoring the denominator to $(t+5)(t-4)$. Thanks in advance.
Note that the signs you wrote are wrong.

$$\frac{1}{t^2-t-20}=\frac{1}{(t\color{red}{-}5)(t\color{red}{+}4)}=\frac 19\left(\frac{1}{t-5}-\frac{1}{t+4}\right)$$
hint: $\dfrac{1}{t^2-t-20} = -\dfrac{1}{9}\cdot \dfrac{1}{t+4} + \dfrac{1}{9}\cdot \dfrac{1}{t-5}$