1. The problem asks why the denominator in the integral expression is $(-4)(-1)$.\n\n2. When integrating a function of the form $f(t) = (100 - t)^{-5}$, we use the power rule for integration: $$\int (100 - t)^n dt = \frac{(100 - t)^{n+1}}{n+1} \times \text{(derivative of the inside function)} + C.$$\n\n3. Here, $n = -5$, so $n+1 = -4$. The integral becomes $$\int (100 - t)^{-5} dt = \frac{(100 - t)^{-4}}{-4} \times \text{(derivative of } 100 - t) + C.$$\n\n4. The derivative of the inside function $100 - t$ with respect to $t$ is $-1$. Since the integral formula requires dividing by the derivative of the inside function, we divide by $-1$, which is equivalent to multiplying by $-1$ in the denominator.\n\n5. Therefore, the denominator is $(-4)(-1)$ because $-4$ comes from the power rule and $-1$ comes from the derivative of the inside function. Multiplying these gives $4$, which simplifies the integral correctly.\n\n6. In summary, the $(-4)(-1)$ appears because of the chain rule in integration: dividing by the exponent plus one and dividing by the derivative of the inner function.