If efficiency is your concern, then creating an Integer object is much more expensive than parsing it. If you have to create an Integer object, I wouldn't worry too much about how it is parsed.
Note: Java 6u14 allows you to increase the size of your Integer pool with a command line option -Djava.lang.Integer.IntegerCache.high=1024 for example.
Note 2: If you are reading raw data e.g. bytes from a file or network, the conversion of these bytes to a String is relatively expensive as well. If you are going to write a custom parser I suggest bypassing the step of conversing to a string and parse the raw source data.
Note 3: If you are creating an Integer so you can put it in a collection, you can avoid this by using GNU Trove (trove4j) which allows you to store primitives in collections, allowing you to drop the Integer creation as well.
Ideally, for best performance you want to avoid creating any objects at all.