Areas can only by positive so this illustration shows the integral of a function and the area between the function and the [math]x[/math]-axis.[br][br]Different functions can be selected with the drop-down and the limits [math]a[/math] and [math]b[/math] can be moved along the axis.[br]The last function on the list can be edited to be any function.[br]Positive integral parts are shown in blue while negative integral parts are shown in a tan color.[br][br][br]There is an option to also show the average value of the function over the interval [math]a[/math] to [math]b[/math].

Move the initial integration point [math]a[/math] so that negative integral parts are formed. [br]How does the integral vary as you move the limits?[br]What happens to the integral and the area if [math]b < a[/math] ?[br]For each function move the limits so that the integral is zero.