A 95 Integra 4dr was garaged \ unused for an extended period (10 months): it seems like one needs to 'stand' on the brakes. What causes this and how can it be corrected?
More than likely it's corrosion on the disk surface. Once it and all the dust from it is gone, the brakes should be pretty much normal, unless there is serious pitting or gouging from the corrosion.
You could pull your brakes apart and clean the surfaces of both the rotor and the pads. To do this, use a wire wheel brush (the type which goes on a drill; I'd use a cup type). Burnish the rotor surface on both sides. Then clean it with some brake clean and a clean shop rag. Just use the wire brush on the brake pads, then blow them off with air (wear a face mask if you do this). If you don't want to use air, brush them off the best you can. Then, reinstall as you took it apart.
The only other thing you can do is replace parts. Until the brakes are clean, your brakes will continue to exhibit poor performance. They can clean up over time, but how long that takes would be unknown.
If the vehicle has power-assisted brakes, the boost unit (vacuum or hydraulic) may not be operating. Sounds like your leg is taking the place of the power-assist. Check vacuum hose to power brake unit. Also, if either the front or rear set of brake calipers has seized up you are functioning with only front or rear brakes. Try low speed panic braking to a stop on loose gravel. Get out and see if all four wheels have dragged through the gravel.