Two very irritating area problems. (polar, and restricted area)

hi guys

1. A curve is given in polar coordinates of r = cos ^ 2 fi , 0 <= fi <= 2 pi

How big area does the place/area have which is enclosed by the curve?.

2. calculate the area of the restricted area which is located between the curves y = x^3 and y = x^4.

Ok as far as I am concerned you don't necesserily need to draw this in x and y axis do I? the thing is how to get to know the limits of integration analytically ? I am very bad at finding stuff like this in graphical solutions