It looks like the flexihose is crimped on the to faucet lines but it's very hard to see on the first image, there seems to be a brass coloured hexagonal piece at the end of the pipe but based on the image I'm unable to tell if it's a crimp or screw fitting.
What would be best at this point is to remove the faucet by disconnecting the hot and cold water flexihoses from your valves and unscrewing the faucet's mounting bolt.
Once you've got the faucet out you can take a closer look at the flexihose connection.
The you'll most likely have one of two situations:
- Either the flexihose is crimped on and it will probably be best to replace the whole faucet.
- Or if you're lucky it will be a screw-in flexihose which can be removed, remove the flexihose and take it to your local hardware store to get a replacement hose. After that it's just a matter of screwing the new flexihose on and mounting the faucet back to the sink.
If you've removed the tap check to make sure the gasket between the tap and the sink is still ok or if it also needs replacing. (Sometimes a good cleaning is enough though!) This will help prevent water leaking down from the top.