Arithmetic expansion

$(( <EXPRESSION> ))

$[ <EXPRESSION> ]

The arithmetic expression <EXPRESSION> is evaluated and the resulting value replaces the whole $((...)) construct:

Please do not use the second form $[ ... ]! It's deprecated. The preferred and standardized form is $(( ... ))!

read -p "Enter first operand: " first
read -p "Enter second operand: " second
echo "The sum is $((first + second))"

Note that in Bash you don't need the arithmetic expansion to simply check for a specific value of an integer, this can be done using the arithmetic evaluation compound command:

read -p "Enter a number: "
if ((number == 1234)); then
  echo "Good guess"
else
  echo "Haha... :-P"
fi

• Introduction to expansion and substitution