It's very easy to calculate this integral. But if you don't know what's integral, there are solution

In-first, i calculated a k
k = (a^2 * b * pi / 8) (or a*a*b*0.39269908169872415480783042290994 :) )
In-second, you should calculate y (or other symbol) from 1 to -1 with division (if n = 5: 1, 3/5, 1/5, -1/5, -3/5, -1)
In-third, calculate F(y) = y*(1 - y^2 / 3). (F(1) = 2/3)
in-fourth, print k*(F(yi) - F(y(i-1))) in loop
example:
if n = 2: first calculate should be k*(F(1) - F(0)), second k*(F(0) - F(-1))
if n = 3: 1) k*(F(1) - F(1/3)); 2) k*(F(1/3) - F(-1/3)); 3) k*(F(-1/3) - F(1))
etc.