  We revisit the analysis of the integrated 2-point functions of local
operators with a $\frac{1}{2}$-BPS Wilson line in $\mathcal{N}=4$ SYM. After
including suitable parity-odd terms in the parametrization of the defect
correlators, we are able to solve the superconformal Ward identities in terms
of an unconstrained function of the cross-ratios. Exploiting this general
solution, we obtain a simple expression of the integration measure for the
integrated correlators with a Wilson line. We test our result by integrating
the available bootstrap expression of the unintegrated correlator at strong
coupling against the predictions of supersymmetric localization, finding
perfect agreement.
