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What integral will you use to find the average? What result do you get? And what ideas do you have about that rectangle?
 
The area of a rectangle is base times height. You know that the base of this rectangle goes from x= -1 to x = 1. How long is this? Multiply this result by the special number so that result will equal the total area. For the record this special number is called the height of the rectangle. What is the total area?
 
The average value of the function \(\displaystyle f\) over the interval \(\displaystyle [a,b]\) is \(\displaystyle \frac{1}{{b - a}}\int_a^b {f(x)dx}\)
\(\displaystyle \int_{ - 1}^1 {{x^2}dx} = \left. {\frac{1}{3}{x^3}} \right|_{ - 1}^1 = \frac{1}{3} - \frac{{ - 1}}{3} = \frac{2}{3}\)
 
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