Antiderivatives

Just as the derivative was a neat party trick to find the slope of the tangent line to a curve at an evaluated point, an antiderivative is an equally impressive party trick capable of finding the area under a curve. One of the most confusing concepts behind the antiderivative is that--much like the derivative--it can be negative; having been taught that distance, area, and volume can never be negative, one has the right to be confused, however, the negative sign simply indicates that the area found is ultimatly mostly under the y-axis.

Another name of the antiderivative is the integral, which makes sence because wheras a derivative is evaluate at a point, an integral is evaluated over an integral, a domain defined by a lower domain value and a higher domain value. Since the area under a curve is zero if the start and end point are the same, the concept of an integral makes sense.

One last concept: since the area can be building for awhile before the analysis, if an initial point is not given then a value of +C is assigned.