1. **State the problem:** We need to find the integral of the function $f(t) = (100 - t)^{-5}$ with respect to $t$. 2. **Recall the formula:** The integral of $x^n$ with respect to $x$ is $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ for $n \neq -1$. 3. **Use substitution:** Let $u = 100 - t$, then $du = -dt$ or $dt = -du$. 4. **Rewrite the integral:** $$\int (100 - t)^{-5} dt = \int u^{-5} (-du) = -\int u^{-5} du$$ 5. **Integrate:** $$-\int u^{-5} du = -\frac{u^{-5+1}}{-5+1} + C = -\frac{u^{-4}}{-4} + C = \frac{u^{-4}}{4} + C$$ 6. **Substitute back:** $$\frac{(100 - t)^{-4}}{4} + C$$ **Final answer:** $$\int (100 - t)^{-5} dt = \frac{(100 - t)^{-4}}{4} + C$$