Derivative and Integral Controllers' Form
Because an integrator, by definition, has a pole at \$s = 0\$.  If the pole has a finite value, then the element is a low-pass filter.

There is a thing called a leaky integrator, where you place the pole at some \$s = -a\$ and \$a\$ is a few orders of magnitude lower in frequency than the anticipated closed-loop bandwidth of your system: this is done to make analog implementations happy, and to some extent for integrator anti-windup.  I don't favor using it at all, but some people love it (and when I was actively consulting, it seemed that any time I said "I never use that technique" the next week I'd be working on a project that demanded it).