You do not need to implement the compareTo methods for the Integer and String classes because they are already implemented and used. All you need to do is fill the array of comparables and that's it, if you call sort on them they will be properly sorted unless the array has mixed types of elements (strings and integers) which you mentioned that wouldn't be the case.
In the documentation you will find that both classes already implement comparable:
. http://docs.oracle.com/javase/7/docs/api/java/lang/Integer.html?is-external=true
http://docs.oracle.com/javase/7/docs/api/java/lang/String.html?is-external=true
Because these classes implement the interface according to polymorphism you can insert them in the mentioned array without any problems.
Strings are compared bases on the String class implementation of the compareTo method which according to the documentation mentioned would be using lexicographic order or they are compared lexicographically.
http://en.wikipedia.org/wiki/Lexicographical_order
Which basically means alphabetic order if all characters are lower case or all characters are upper case, and the characters with lower ascii value becoming smaller in comparison.