How != and == operators work on Integers in Java?

The following code seemed really confusing to me since it provided two different outputs.The code was tested on jdk 1.7.

public class NotEq {

public static void main(String[] args) {

    ver1();
    System.out.println();
    ver2();
}

public static void ver1() {
    Integer a = 128;
    Integer b = 128;

    if (a == b) {
        System.out.println("Equal Object");
    }

    if (a != b) {
        System.out.println("Different objects");
    }

    if (a.equals(b)) {
        System.out.println("Meaningfully equal.");
    }
}

public static void ver2() {
    Integer i1 = 127;
    Integer i2 = 127;
    if (i1 == i2) {
        System.out.println("Equal Object");
    }

    if (i1 != i2){
        System.out.println("Different objects");
    }
    if (i1.equals(i2)){
        System.out.println("Meaningfully equal");
    }
}

}

Output:

[ver1 output]
Different objects
Meaningfully equal.

[ver2 output]
Equal Object
Meaningfully equal

Why the == and != testing produces different results for ver1() and ver2() for same number much less than the Integer.MAX_VALUE? Can it be concluded that == checking for numbers greater than 127 (for wrapper classes like Integer as shown in the code) is totally waste of time?