5.3 The Fundamental Theorem of Calculus/31

$\int _{0}^{\frac {\pi }{4}}\sec ^{2}(t)\,dt=\int _{0}^{\frac {\pi }{4}}sec^{2}(t)dt=tan({\frac {\pi }{4}})-tan(0)=1-0=1$

Therefore, $\int _{0}^{\frac {\pi }{4}}sec^{2}(t)dt=1$

(Use FTC #2,) $\int _{a}^{b}f(x)dt=F(b)-F(a)$