Net change in accumulated stress via the Net Change Theorem

By the Net Change Theorem, the total change equals $\int_0^{\pi/4} \sec^2(x)\,dx$. This directly represents the accumulated change in $F$ over the interval, since $F'(x) = \sec^2(x)$ is the rate of change.

An antiderivative of $\sec^2(x)$ is $\tan(x)$, so $\int_0^{\pi/4} \sec^2(x)\,dx = \tan\left(\frac{\pi}{4}\right) - \tan(0) = 1 - 0 = 1$. Thus the total change in accumulated stress from $x=0$ to $x=\pi/4$ is $1$.