solution

Well the force $f$ exerted by a spring varies with it's displacement from equilibrium $x$, as $f(x) ~=~ -kx$, where k is the spring coefficient. The anti-derivative of $-f(x)$ is ${1\over 2}k x^2$ plus a constant. We can for convenience set the additive constant to zero, so that

$$U_{spring} ~=~ {1\over 2}k x^2$$ (1.33)