%Three term Legendre root and co-efficients
x1 = 0.7745966692
x2 = 0.0000000000
x3 = -0.7745966692
c1 = 0.5555555556
c2 = 0.8888888889
c3 = 0.5555555556

%The integration interval is normalised to -1 to 1
function y = myFunc(x)
  y = (sin((0.55*x+2.05)/2) - 1)^2;
endfunction

approx_integral = c1*myFunc(x1) + c2*myFunc(x2) + c3*myFunc(x3)