A somewhat better attempt:
I split the integral up in two for simplicity.
Let n go to infinity and we have proved convergence.
Still working on the other part though.
1. Given the sequence and function . show that
2. How can we use this to deduce that (with the max norm) is not complete.
2. The limit isn't in C[-1,1] so its not complete...
Very bad I know.
Any suggestions are welcome.