Originally Posted by D_hodough

The area of the shaded region is 6.5/3...

or 2.1666666666666... units.

[negative of (the integral from -.5 to 0 of 4-(x^2) minus the integral of -.5 to 0 of (x^2) - 2x)]
= [negative of (4x - (x^3)/3 from -.5 to 0) - ((x^3)/3 - (x^2) from -.5 to 0]
= -[(0 - (2 - .125/3)) - (0 - (.125/3 - .25)]
= -[0 - 2 +.125/3 - 0 + .125/3 - .25]
= 2 - .25/3 + .25
= 6.5/3, if I'm not mistaken...

Someone say something about North Americans? :-P