JDK8 source code

/** * Returns an {@code Integer} object holding the value * extracted from the specified {@code String} when parsed * with the radix given by the second argument. The first argument * is interpreted as representing a signed integer in the radix * specified by the second argument, exactly as if the arguments * were given to the {@link #parseInt(java.lang.String, int)} * method. The result is an {@code Integer} object that * represents the integer value specified by the string. * * 
In other words, this method returns an {@code Integer} * object equal to the value of: * * 
 * {@code new Integer(Integer.parseInt(s, radix))} * 
 * * @param s the string to be parsed. * @param radix the radix to be used in interpreting {@code s} * @return an {@code Integer} object holding the value * represented by the string argument in the specified * radix. * @exception NumberFormatException if the {@code String} * does not contain a parsable {@code int}. */ public static Integer valueOf(String s, int radix) throws NumberFormatException { return Integer.valueOf(parseInt(s,radix)); }

Using Inteager to illustrate here, valueOf actually calls parseInt.
The parseInt method is a static method of the Integer class. Its function is to convert a string into an integer.int
valueOf is also a static method of the Integer class. Its function is to convert a string into anInteger object.