Chapter 5.5, Problem 1E

In $C\left[a,b\right]$ , define the product $\langle f,g\rangle ={\displaystyle {\int }_a^{b}f\left(t\right)g\left(t\right)dt}$ .
Show that this product satisfies the property $\langle f,g\rangle >0$ for all nonzero f.