Concrete is a flexible building material during construction, and a nightmare to repair once poured. If you wish to reuse the portion 'broken' off, you'll need a pry-bar to lift. If you don't care to keep the broken portion then use a sledgehammer and knock it into pieces you can handle. If there's a crack in your slab then it may be from settling. Depending on how much it has settled you can 'fix' it by applying grout into the crack (assuming the crack is around 13mm (1/2") or less. If the crack is larger there may be larger then you may need to lift the broken portion and re-level the base, this is more work and re-leveling may be finicky. If you lift and re-level it's a good idea to grout between the detached piece as well when reinstating the corner. Consider that almost any repair to concrete is going to look inconsistent. The grout method will look like a fill in the gap, a new pour will look newer compared to the older stuff, and lifting the portion and re-leveling the broken corner may result in a corner that heaves in freezing weather. If your walk is older it may be time for a new walkway, maybe something different. Good luck.