evaluate the integral.\n int_{0}^{1}(u + 4)(u - 5)du

Explanation:

Step 1: Expand the integrand

$$(u + 4)(u - 5) = u^2 - u - 20$$

Step 2: Integrate term-by-term

$$\int_0^1 (u^2 - u - 20) , du = \left[ \frac{u^3}{3} - \frac{u^2}{2} - 20u \right]_0^1$$

Step 3: Evaluate at bounds

Substitute upper bound (u = 1):
$$\frac{1^3}{3} - \frac{1^2}{2} - 20(1) = \frac{1}{3} - \frac{1}{2} - 20$$
Substitute lower bound (u = 0) (result is (0)):
$$\left( \frac{1}{3} - \frac{1}{2} - 20 \right) - 0 = -\frac{1}{6} - 20 = -\frac{121}{6}$$

Answer:

(-\dfrac{121}{6})