Let g be an integrable functions on [0,1] and $\displaystyle 1/p+1/q=1$ with $\displaystyle 1<p<\infty$. Suppose that there is a constant $\displaystyle M>0$ such that $\displaystyle |\int fg| \leq M||f||_p$ for all bounded measurable functions $\displaystyle f$. Prove that $\displaystyle g \in L^q$ and $\displaystyle ||g||_q \leq M$.

any help is appreciated please.