  The theoretical uncertainty of $(g-2)_\mu $ is currently dominated by
hadronic contributions. In order to express those in terms of directly
measurable quantities, we consider a sum rule relating $g-2$ to an integral of
a photo-absorption cross section. The sum rule, attributed to Schwinger, can be
viewed as a combination of two older sum rules: Gerasimov-Drell-Hearn and
Burkhardt-Cottingham. The Schwinger sum rule has an important feature,
distinguishing it from the other two: the relation between the anomalous
magnetic moment and the integral of a photo-absorption cross section is linear,
rather than quadratic. The linear property makes it suitable for a
straightforward assessment of the hadronic contributions to $(g-2)_\mu $. From
the sum rule we rederive the Schwinger $\alpha/2\pi$ correction, as well as the
formula for the hadronic vacuum-polarization contribution. As an example of the
light-by-light contribution we consider the single-meson exchange.
