-----Description-----  
This task involves computing the average of two integers. The objective is to determine a value that closely approximates the true arithmetic mean when using integer division, ensuring that the result reflects the necessary rounding behavior.

-----Input-----  
The input consists of:  
• a: An integer.  
• b: An integer.

-----Output-----  
The output is an integer representing the computed average of a and b using integer division.

-----Note-----  
The specification requires that the computed average satisfies the condition that 2 * avg is between (a + b - 1) and (a + b + 1), ensuring that the result meets the expected rounding boundaries.