You will also need to add the library as a dependency to the module that needs it.
Choose Project Settings > Modules. Select the Module that needs the library (in your case it seems like you have only one module in your project, ChatBot). Select the Dependencies tab. Click the '+' button and choose Library...). Finally, select the mysql-connector.. library that you added to the project.
Edit: I see now that this wasn't your problem at all. The problem with your code is that you have an unhandled exception from Class.forName(). The method can throw the checked exception: ClassNotFoundException, which must be handled by adding a catch or by adding throws ClassNotFoundException to the method signature of getConnection().
In such cases with error in the code, the easiest way to figure out what's wrong to simply move the caret to the code with the red squigly line and see what IDEA says in the bottom status bar. Alternatively you can hover the mouse pointer above it and the error message is presented as a popup.