Chapter 4 - Integrals - 4.4 Indefinite Integrals and the Net Change Theorem - 4.4 Exercises - Page 337: 32

$-\frac{5}{4}$

We use the derivative formula for $sec \theta $ $$\frac{d}{dx} sec \theta = sec \theta tan\theta$$ to evaluate the given integrand Now, we substitute $\frac{\pi}{4} $ and $0$ into $\theta$ and get $sec(\frac{\pi}{4}) - sec0 = $ $-\frac{1}{4} - 1 = -\frac{5}{4}$