Retrieving input effective radius from Sérsic profile
The conceptual problem is that the half-light radius is the radius of a circle enclosing half the total light, assuming that the object is circular with a radial intensity profile equal to the Sersic function. 

So you need to integrate over circular rings, each of which has an area of $2 \pi r \, dr$ and an intensity (or surface brightness) of $S(r)$:
$$L(&lt; R) = \int_{0}^{R} 2 \pi r \, S(r) \, dr$$
where $S(r)$ is the Sersic function evaluated at radius $r$.

Instead, you're just doing the integral of a line of fixed width:
$$\int_{0}^{R} S(r) \, dr$$

In Python terms, the (pre-calculated) function you integrate should be

I = 2 * np.pi * x * Sersic(x)


not

I = Sersic(x)


(Alex is also correct that you have almost no resolution near the value of r_eff that you are trying to find.)