What could these mysterious hoses be sticking out of the ground?
Whatever they are, as long as they are both coming 'out' of the ground and they are both open-ended, they are no longer used for anything. The easiest thing to do would be to cut them off a little under ground level and forget about them.
Another though would be to stick your garden hose in each one and see if you can find the water running out somewhere around your property. That would show you that they are drain hoses and drain somewhere. Then you know for sure what they are.
A corrogated hose is almost always a drain, I gree with others that it's probably from an old sump, or possibly a separate drain for something. I bought a house years ago where the people hooked up their washing machine discharge water to the same type of hose, and drained it along the ground into the adjacent farmer's field. Completly wrong, but that's what they did. If you ever have wet basement probelms, it could be a secondary drain hose that was only used as a second system to the sump pump on very rainy days. It would make sense they would cut it and hide it before you bought the house. They wouldn't want you to know about it.
The smooth black hose could be anything but usually smooth hoses like that are used to draw water, not drain it.
Who knows? Like I said, if you really want to know where they go, fill them with the garden hose, wait a while, and walk around and look.