How Does an Imperfect Spring Affect the Velocity of a Released Ball?

[endeavor]

The force required to compress an imperfect horizontal spring an amount x is given by F = 150x + 12x³, where x is in meters and F in Newtons. If the spring is compressed 2.0m, what speed will it give to a 3.0 kg ball held against it and then released?

I know how to integrate F(x) to get the work done, and with that I could use the work-energy theorem to find the speed. But do I take the lower limit of the integral as x = 2.0 and the upper limit as x = 0?
But then the integral would be negative and 1/2mv² can't be negative...

 

[Mindscrape]

Are you finding the work function by solving F = -\frac{dU}{dx}? I would integrate from x=0 to x=x to find the general solution, but if you wanted to put in 2 right away then that would work. The negative thing depends on where you define your zero potential.