why Integer.MAX_VALUE + 1 == Integer.MIN_VALUE?

You must understand how integer values are represented in binary form, and how binary addition works. Java uses a representation called two's complement, in which the first bit of the number represents its sign. Whenever you add 1 to the largest java Integer, which has a bit sign of 0, then its bit sign becomes 1 and the number becomes negative.

This links explains with more details: http://www.cs.grinnell.edu/~rebelsky/Espresso/Readings/binary.html#integers-in-java

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The Java Language Specification treats this behavior here: http://docs.oracle.com/javase/specs/jls/se6/html/expressions.html#15.18.2

If an integer addition overflows, then the result is the low-order bits of the mathematical sum as represented in some sufficiently large two's-complement format. If overflow occurs, then the sign of the result is not the same as the sign of the mathematical sum of the two operand values.

Which means that you can rely on this behavior.

Because the integer overflows. When it overflows, the next value is Integer.MIN_VALUE. Relevant JLS

If an integer addition overflows, then the result is the low-order bits of the mathematical sum as represented in some sufficiently large two's-complement format. If overflow occurs, then the sign of the result is not the same as the sign of the mathematical sum of the two operand values.

The integer storage gets overflowed and that is not indicated in any way, as stated in JSL 3rd Ed.:

The built-in integer operators do not indicate overflow or underflow in any way. Integer operators can throw a NullPointerException if unboxing conversion (§5.1.8) of a null reference is required. Other than that, the only integer operators that can throw an exception (§11) are the integer divide operator / (§15.17.2) and the integer remainder operator % (§15.17.3), which throw an ArithmeticException if the right-hand operand is zero, and the increment and decrement operators ++(§15.15.1, §15.15.2) and --(§15.14.3, §15.14.2), which can throw an OutOfMemoryError if boxing conversion (§5.1.7) is required and there is not sufficient memory available to perform the conversion.

Example in a 4-bits storage:

MAX_INT: 0111 (7)
MIN_INT: 1000 (-8)

MAX_INT + 1:

 0111+
 0001
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 1000