The bumpers are a plastic that is flexible. The cracks are likely from bumping things, or freeze-thaw, where the bumper was more flexible than the paint.
If the cracks are not actually in the plastic, but just in the paint surface, you would have to simply touch up the paint. Though cracks could likely occur there again. You may want to take the easy of flexing of the paint into consideration when you choose a paint to use.
I've never painted a car so I'm not sure what all your options could be.
If the cracks are in the bumper, there are repair kits at shops to fill cracks and seal them up. So you would need to do that.