$a)$ $C^1[0,1]$ of continuously differentiable real valued functions on $[0,1]$ with the metric $d(f,g)=\max_{t\in[0,1]}|f-g|$
I am sure that it is not complete, but could any one help me to construct a counter example? well, $f(x)=|x-1/2|$ will work?
$b)$ The space of all polynomial with real coeffi single variable with same metric as above, this is also not complete, $|x-1/2|$ will work?