The ReadMail class has been written to connect to the email service , read the messages from the server and write the messages in text to System.out.
It does all of this in one call to its constructor.
That isn't going to be useful to you in a web application.
I think you need to refactor your ReadMail class.
At a minimum you need to split out the "creation of the object", "reading of messages" and the "printing of messages" into seperate operations so that you can invoke it something like:
Once you have done that then your JSP should be able to construct a ReadMail object, and call the readMessages() method.
You then add logic to the JSP to display those messages appropriately.
Note that the JSP should probably NOT use the ReadMail class to print out the messages. That is what JSPs are for - displaying java objects.