Question 23332
To solve this problem, think about graphing the quadratic {{{x-x^2}}}.  

{{{ graph( 200, 200, -2, 2, -2, 2, x-x^2) }}}

Now we look at which x values gives a positive output, or which x values have a y value that is above the x axis.  This yields the interval [0,1] as the answer.

Where does 0 and 1 come from?  They're the solutions to the equation 0 = {{{x-x^2}}} = x(1-x).  So x = 0 or 1-x = 0.  Thus x = 0 or 1.