What does an integral actually describe, in visual terms?

Answer 1

the area under a curve between two points.

Answer 2

In numeric terms: the plot of the integral function can be broken down into little "rectangles" of height (y=f(x)) times delta x, extending from the upper to lower limit in the problem, for each xi selected to form the width of a given rectangle. The sum of these rectangles as delta x goes to zero yields areas above and below the y-axis. The algebraic sum of these areas equals the integral.

Answer 3

When you take an integral of a function with lower and upper bounds, you are finding the "area under the curve", i.e. graphically, the area between the curve on the graph of the function and the x-axis.

Answer 4

It is the area under the curve.

Check out the link below. The integral of the function f(x) from the boundary a to b is the shaded region S.