Evaluate a definite integral of sec^2(x) using the Fundamental Theorem of Calculus

Since $\frac{d}{dx}[\tan(x)] = \sec^2(x)$, the function $F(x) = \tan(x)$ is an antiderivative of $f(x) = \sec^2(x)$. By FTC Part 2, $\int_0^{\pi/4} \sec^2(x)\,dx = \tan(x)\Big|_0^{\pi/4} = \tan(\pi/4) - \tan(0)$.

Evaluating the antiderivative at the bounds gives $\tan(\pi/4) = 1$ and $\tan(0) = 0$. Subtracting, $1 - 0 = 1$, so the value of the definite integral is $1$.