My brakes are very spongy/mushy. In order for them to engage sufficiently I have to press down pretty far. However, If I pump them and build pressure then they work very crisp without that spongy feeling.

 

deleted

 

How would I check this?

 

You might try bleeding them at the caliper bleed screws or maybe changing the fluid out completely. Seems to me, if it were a vacuum/booster leak, the pedal would feel harder because you're just pushing the fluid around with your foot at that point. The spongy feeling you describe makes me think there's air in there someplace or maybe a leaky master cylinder or some such. What's the level of the fluid in the reservoir look like? What does the fluid itself look like?

 

^^ I was thinking of air in the brake lines, too. That's where I would start.