Dupre,
Not quite right about (mature) forests being steady-state and not sequestering carbon. Forest detritus builds up (some of the carbon indeed recycles into the atmosphere, but some does not), eventually (geological timing) gets buried, eventually turns into coal and/or hydrocarbons.
A mature forest does indeed suck up carbon from the atmosphere. Immature forests suck up even more (net), because the forest mass (trunks, leaves etc) increases, and has a large carbon component.