In, class when we were attempting questions in which we used to find area bounded by curves through definite integrals, we used to look for the interval in which the function would be negative, then we'd Divide the whole GIVEN INTERVAL into Sub-intervals in which the function was either positive OR negative. We then used to calculate the areas in these subintervals and from here the confusing part starts...

We put a negative sign with the areas under the x-axis, and then added them to the rest of the areas...fair enough and we understood what it meant....

HOWEVER, when we were solving simple definite integrals (where we were not asked about area) we did not care abt the values for which the function was positive...Instead, we just solved it by putting in the limits of the integral and we got the answer......

Im now abit confused?...Why didnt we care for the "negative values of the function" in solving SIMPLE DEFINITE INTEGRALS, just like we did in solving INTEGRALS FOR AREAS?

By the way....Nevermind.......