Evaluate ${\displaystyle \underset{0}{\overset{1}{}}}(x-x^2)dx$

a$.$ Divide the integration domain into four parts and use Riemann sum to give an upper bound and a lower bound of the integral.

b$.$ Give the exact value of the integral.

c$.$ How do the bounds you obtained compare with exact value? How would the difference behave as you divide the integration domain into more parts?