This is the definition of impulse. It states that the impulse due to a force is equal to the force times the time interval during which that force is applied. For this equation to hold true, the force must be a constant, or, one must use the average force for the time interval.
Darn it! By convention, the symbol used to represent impulse is not a good reminder of what it is. Impulse begins with an "I" but we use the letter "J" to represent impulse.