Answer
False.
Work Step by Step
All rational numbers are integers.
Integers: {..., -3, -2, -1, 0, 1, 2, 3, ...}
Rational Numbers: Any number that can be expressed as $\frac{a}{b}$.
Integers are whole numbers. A rational number example is $\frac{1}{3}$. It's a rational number, but not an integer.
The statement is false.