First, for both (first == second)，因为 first 是 int（基本类型），所以在进行 == 比较的时候，second 会从 Integer 拆箱为 int，然后 == 进行的是值比较 —— 因为两次值（第一次都为 127，第二次都为 128）都相等，所以两次都是 true;

Looking at the source code of two (second == third)，second 和 third 都是 Integer（对象），所以 == 比较的时候，比较的是对象的引用，如果两个引用指向的是同一块内存（同一个对象），那么返回 true，否则返回 false。
second = 127; 这样的代码其实是 Java 的语法糖，真正执行的是 second = Integer.valueOf(127)，我们来看看 Integer.valueOf:

It's easy to understand, Integer 的内部缓存了 IntegerCache.low ~ IntegerCache.high 的 Integer，所以如果传入的整数参数 i 在这个范围之内的话，那么返回的就是缓存的对象，否则才新建一个 Integer。在 Oracle 的 JVM 上，Integer 的缓存范围默认为 -128 ~ 127。所以每次调用 Integer.value(127) 返回的都是同一个被缓存的 Integer，而调用 Integer.value(128) 将每次新建一个 Integer（new Integer(128)）。所以第一个(second == third) returns true and the second one returns false.

Two Ineger types are compared with ==. If the value is between -128~127, it returns true, otherwise it returns false. This is due to the buffer object of Integer.valueof().

    public static Integer valueOf(int i) {
        if (i >= IntegerCache.low && i <= IntegerCache.high)
            return IntegerCache.cache[i + (-IntegerCache.low)];
        return new Integer(i);
    }

    private static class IntegerCache {
        static final int low = -128;
        static final int high;
        static final Integer cache[];

        static {
            // high value may be configured by property
            int h = 127;
            String integerCacheHighPropValue =
                sun.misc.VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
            if (integerCacheHighPropValue != null) {
                try {
                    int i = parseInt(integerCacheHighPropValue);
                    i = Math.max(i, 127);
                    // Maximum array size is Integer.MAX_VALUE
                    h = Math.min(i, Integer.MAX_VALUE - (-low) -1);
                } catch( NumberFormatException nfe) {
                    // If the property cannot be parsed into an int, ignore it.
                }
            }
            high = h;

            cache = new Integer[(high - low) + 1];
            int j = low;
            for(int k = 0; k < cache.length; k++)
                cache[k] = new Integer(j++);

            // range [-128, 127] must be interned (JLS7 5.1.7)
            assert IntegerCache.high >= 127;
        }

        private IntegerCache() {}
    }

    /**
     * Cache to support the object identity semantics of autoboxing for values between
     * -128 and 127 (inclusive) as required by JLS.
     *
     * The cache is initialized on first usage.  The size of the cache
     * may be controlled by the {@code -XX:AutoBoxCacheMax=<size>} option.
     * During VM initialization, java.lang.Integer.IntegerCache.high property
     * may be set and saved in the private system properties in the
     * sun.misc.VM class.
     */

• Comparison between objects will affect the results due to buffering within a certain range.

• Comparison between packaged class (object) and basic type is a direct ratio to get the result.