The Integral of a function determines the area under a curve of the function.
It does this by breaking up the function into rectangular sections, and computing the area of each section. By making the rectangular sections infinitely narrow, and summing them, it is able to compute the exact area under the curve.
The starting point of integration is indicated just below the integration sign, and the ending point is above the integration sign. Note that a function may have negative area if it decreases below 0.