"Thinking backwards" shows up in a lot of places. That means it must be important! Here, "thinking backwards" means instead of using a known integral value to evaluate an expression, we'll work backwards from an equation to find the integral value.
Think of the integral you're looking for as a unit. Instead of solving for x, you'll be solving for something like 
. If your equation contains a slightly different integral than the one you want, use the properties to manipulate the integral until it's what you're looking for.