Let $X$ be the normed space of all real polynomails in one variable, with $||f||=\int_0^1 |f(t)|dt$. Put $B(f,g)=\int_0^1 f(t)g(t)dt$, and show that $B$ is a bilinear functional on $X\times X$ which is separately continuous but is not continuous.
I have done for proving that $B$ is the bilinear functional and seperately continuous. But I cannot show that $B$ is not continuous. Could someone help me, please? Thanks advance.