Chapter 4 - Integrals - 4.3 The Fundamental Theorem of Calculus - 4.3 Exercises - Page 328: 51

$f(\theta)=\sec\theta\tan\theta$ is not continuous in $(\pi/3,\pi)$, and hence FTC-2 cannot be applied.

According to the fundamental theorem of calculus, $\int_a^bf(x)dx = F(b)-F(a)$, where $F$ is the antiderivative of $f$ or $F'=f$, provided that $f$ is continuous in $(a, b)$. Here, $\sec\theta\tan\theta$ is not continuous in $(\pi/3,\pi)$ and has an infinite discontinuity at $\theta=\pi/2$.