I'm not sure, but I think this might be something known as the "average value"
For instance......let us find the area of the curve between the function 1 - x^2 and the x axis
The curve will intercept the x axis at x = - 1 and x = 1
So.....using symmetry, the area is
1 1
2* ∫ 1 - x^2 dx = 2 [ x - (1/3)x^3 ] = 2 [ 1 - 1/3] = 2 [ 2/3] = 4/3 units^2
0 0
Note that we can construct a rectangle with the same area if we let the width range from x = - 1 to x = 1 = 2 units = the interval width
So....the height of this rectangle must be (4/3) / 2 = 4/6 = 2/3
See this image :
Note that the rectangle ABCD has the same area as the definite integral
To always find this average value we can calculate this :
[ area of integration ]
_________________ = height of rectangle = average value
interval width