The "buzzing" sound you hear when you first start your car is the ABS system pressurizing. This only pertains to '94-'97 Integras, because they have a different ABS system from the '98-'01 Integras and '97 Type-Rs. The '94-'97 Integra's ABS system has a seperate brake fluid reservior (#3 in diagram). The ABS brake fluid should be bleed and flushed periodically to remove air from the system. If you hear the buzzing for more than a couple of seconds (~2-5 sec.), this is a good indication that the ABS system needs to be bleed. Now if you hear the buzzing for ~60 seconds and then it shuts off and the ABS light comes on, it means that the ABS system could not be pressurized and the ABS has been disabled. The main cause is a small rubber O-ring (#23) which seals the brake fluid ACCUMULATOR (#2) which is under extremely high pressure. If this O-ring fails brake fluid will leak out and you will see it under the ABS module.

Here is a diagram of the '94-'97 Integra ABS module: