A definite integral may or may not represent area. It depends on the context of the question.

If you're asked to evaluate the area, then you will need to add all the absolute values of the definite integrals (which is equivalent to subtracting the negative definite integrals) because there is no such thing as negative area.

However, if you are simply asked to find a definite integral, it may be for some other purpose, so you would just evaluate the definite integral as is.