Yeah, it's very difficult problem. We have to plot a function what contain a other unknown function as u(t).
If I understand well your step function jump at origin from 0 to 1. Therefore the function a(t) has two irregular point: t=1 and t=-1. You able to plot piece by pice such as [-inf -1], [-1 1], [1 inf]. During the intervals a(t) behaves as normal function.