Showing an isometric isomorphism between $C([0,1])$ with sup norm to itself

Question

Let $T:C([0,1])\rightarrow C([0,1])$ defined by

$Tf (t) = f(t) + \int_{0}^{t} f(s) ds$,

It is easy to show that $T$ is a linear and continous operator, but I'm stuck about showing injective,surjective or exhibiting its inverse. How can i compute those things?