If f is a continuous function on [a, b], and F is any antiderivative of f, then:
∫ab f(x) dx = F(b) - F(a) = F(x) |ab
The average value of a continuous function f over the interval [a, b] is given by:
1/(b - a)∫ab f(x) dx
The average value is the height of the rectangle of width b - a that has the same area as the area under the graph of f(x) from x = a to x = b.