Which of the following options defines an integer variable?

The selection of "C. int age;" correctly defines an integer variable because it uses the appropriate syntax for declaring a variable of type integer in many programming languages, including C, C++, and Java. The keyword "int" specifies that the variable 'age' will store integer values, which can be used for numeric calculations without decimal points.

In the context of programming, variable types must be defined correctly to ensure that the compiler or interpreter understands what kind of data the variable will hold. The definition in option C follows the conventional data type declaration practices, where "int" is a standard type representing integer values.

The other options do not conform to this standard variable declaration syntax for defining integers. "A. char age;" declares a variable of type character, suitable for holding single characters or small strings. "B. integer age;" uses a non-standard keyword "integer," which may cause confusion, as many languages use "int" instead. Lastly, "D. age: int;" incorrectly uses a colon instead of the correct syntax for type declaration, which results in a syntax error.