The Average Value of a Function G on 0 $\le$ X $\le$

Multiple Choice

The average value of a function g on 0 $\le$ x $\le$ 2 is a constant $\bar{g}$ given by $\bar{g}=\frac{1}{2-0} \int_{0}^{2} g(d) d x$ .Also, $\int_{0}^{2}(g(x) -\bar{g}) ^{2} d x \geq 0$ , since $(g(x) -\bar{g}) ^{2}$ is a square.Which of the following must be true?

A) $\left(\int_{0}^{2} g(x) d x\right) ^{2} \leq \int_{0}^{2}(g(x) ) ^{2} d x$
B) $\left(\int_{0}^{2} g(x) d x\right) ^{2} \geq \int_{0}^{2}(g(x) ) ^{2} d x$
C) $\left(\int_{0}^{2} g(x) d x\right) ^{2}=\int_{0}^{2}(g(x) ) ^{2} d x$
D) None of these