If by "broken" you mean that the screen is physically damaged due to accident or abuse, then no, Apple will not service it for free. If you have AppleCare+ for the iPad, Apple will replace it for the AppleCare+ fee standard for the plan in your country; it's $49 in the US.
Otherwise, Apple does not repair iPads, but will replace the entire iPad for their flat out-of-warranty replacement fee; see the Repair Pricing section here:
There are independent iPad repair services that may be able to replace the screen for less. Do a web search for "ipad repair". Note, though, that if you elect to have the iPad serviced by an unauthorized shop, all further warranty will be void.