I find the statement that the normed, complex or real, linear space $C[a,b]$ is reflexive, i.e. the natural map of the space $C[a,b]$ into the bidual space $C[a,b]^{\ast\ast}$, defined by $\pi:C[a,b]\to C[a,b]^{\ast}$, $x\mapsto \psi\_x$, where $\psi\_x:C[a,b]^{\ast}\to K$, $f\mapsto f(x)$, is surjective.

I have found nothing about the issue. Can anybody suggest a link with a proof -as elementary as it is possible, since I'm just beginning to study those areas of mathematics, but my book states a lot and proves only a part of what it states- or a direct proof of the statement?

$\infty$ thanks!!!