While integrated bras are often referred to as shelf bra, this terminology is not correct.
Instead, it is a very specific type of bra that is also a kind of machine. It includes support for the rope, but does not have any kind of coating material of the upper part of the chest. As such, these bras are not practical for everyday use, although many lingerie stores worldwide selling a wide selection of them. Whether or not a shelf bra will work for you depends on the type you choose.