Show that this metric space is incomplete: $C[0,1]$ with metric defined as follows: $d(f,g) = \int_0^1 |f(x)-g(x)| \mathrm{d}x$
$C([0, 1])$ is not complete with respect to the norm $\lVert f\rVert _1 = \int_0^1 \lvert f (x) \rvert \,dx$