How do you find the parameterization of this curve

How is the parametrization of the second path found.

http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsPtI_files/image002.gif

It's 1- x^3.

I want an explanation.

He explains it on the first page of that section. If you have a polynomial function of the form

y = f(x)

Then all you have to to obtain the parametrization is to let x = t. Then the parameters are:

x = t
y = f(t)

So in that example, we let x = t. Then y = 1 - t^3. That's it.

Done!

P.S. Obviously it's more complicated for circles and things like that, but for polynomials, it's really just that simple.