Brother: U& Twfx too smart ,I do it by tipical math.

Let 20=1,60=3. 3 periods.[0,1],[1,2] and [2,3]
[0,1]:
p(x)=(1+x)/3. Intg(1+x)/3 from 0 to 1,It is 1/2
[1,2]:
p(x)=2/3 ....it is 2/3
[2,3]:
p(x)=(2-x)/3.........it is 1/2.
1/3(1/2+2/3+1/2)=5/9.
Sorry ,I'm too old to do by heart.