We can divide the denominator into the numerator to get:
1-(2x+1)/(x²+x+1). When this is integrated wrt x we get:
x-ln|x²+x+1|+C where C is constant of integration, because the numerator is the derivative of the denominator.
Apply the range:
(1-ln(3))-0=1-ln(3)=-0.09861 approx.