Well, the API for Integer.valueOf(String) does indeed say that the String is interpreted exactly as if it were given to Integer.parseInt(String). However, valueOf(String) returns a new Integer() object whereas parseInt(String) returns a primitive int.
If you want to enjoy the potential caching benefits of Integer.valueOf(int), you could also use this eyesore:
Integer k = Integer.valueOf(Integer.parseInt("123"))
Now, if what you want is the object and not the primitive, then using valueOf(String) may be more attractive than making a new object out of parseInt(String) because the former is consistently present across Integer, Long, Double, etc.