= Solution
For the resonant contribution only, subtract nonresonant <Bhabha scattering> and its interference before interpreting a fitted area. The <integrated narrow vector resonance area> follows from the <Breit-Wigner resonance cross section>, with $J=1$, $s_{e^-}=s_{e^+}=1/2$, and $p\simeq M/2$, becomes
$$
\sigma_{ee}(E)=\frac{3\pi}{M^2}\frac{\Gamma_{ee}^2}{(E-M)^2+\Gamma^2/4}.
$$
Across a narrow <scattering resonance>, treat the prefactor and partial <decay widths> as constant and extend the integral over $E-M$ to the real line. Since $\int_{-\infty}^{\infty}du/(u^2+a^2)=\pi/a$,
$$
\mathcal I_{ee}\equiv\int\sigma_{ee}(E)\,dE=\frac{6\pi^2}{M^2}\frac{\Gamma_{ee}^2}{\Gamma}=\frac{6\pi^2}{M^2}B_{ee}^2\Gamma,\qquad
\Gamma=\frac{M^2\mathcal I_{ee}}{6\pi^2B_{ee}^2}.
$$
A normalized beam-energy response convolves the line shape without changing this full area. It can completely change the observed peak height and apparent width. If a uniform acceptance $\epsilon$ is not already unfolded, use $\mathcal I_{ee}=\mathcal I_{ee}^{\rm obs}/\epsilon$. The distinction between $B_{ee}^2$ for this exclusive final state and $B_{ee}$ for an inclusive final state is essential.
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