Piet,

Your squeaking noises are coming from you brake pads rubbing against your rotor. And the reason why they're rubbing is probably because your caliper is sticking.

You have glide pins in your calipers that may be getting rusty, and are not releasing properly. Typically, there are rubber boots that keep out moisture and brake dust that can contribute to the onset of rust. Your best bet is to remove your caliper and thoroughly clean all moving parts. Add grease to the glide pins and replace any worn dust boots.

You should also check your brake line to that caliper. If it is looking really worn, replace it. Because of all the rubbing, your pads may need to be replaced and your rotor may need to be turned (machined).

Depending on the age and wear of the caliper, pads and rotor, all three things may need to be replaced. And when you replace one side, you should replace the other side to keep your braking system at peak performance. It can get a little pricy, but it'll be worth it.

Any mechanic can perform this task. Now that you know what the problem is, you can simply ask the mechanic to condition the caliper where your squeaks are coming from. If they just need to clean the caliper and say your rotor and pads look fine, it'll be a very quick and inexpensive fix.

Good luck!
Anthony