It's a good question, and one where I actually have an answer too.
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Photo © Colin Abbott
In the Nov/Dec 2000 issue of Airliners Magazine the exact same question was asked and here is what they had to say...
"Those rectangular areas contain antennae, vents, intakes and exhausts. Leaving the sections unpainted avoids the additional maintenance costs incurred to mask off each item for painting. Also, water and slush are kicked up by the nose gear and various fluids are used in aircraft operation tend to pool in these areas. The fluids take a toll on the finish and corrode the paint. United periodically washes and seals aircraft exteriors and paint crews perform touch-up work when necessary. The traveling public only sees this area of the aircraft when it passes overhead.
Instead of a sealant, United's Airbus aircraft rely on exterior paint as corrosion protection. Therefore, the UA A319 and A320 fleet contain a solid-blue underside, unlike the Boeings."