Need some clarification

Agree that anR stands for the average value of f[x, y, 2] as {x, y, z} varies through a specied solid region R in xyzspace. The formula for \"this I111 dxdydz How do you know that ava is a number that falls between the minimum value of f[x, y, z] on R and the maximum value of f[x, y, z] on R