Question

How is carbon reintroduced into the atmosphere?

Answer 1

Usually by rotting or burning.

Explanation:

Oxydation -- this can be by rotting or by burning -- converts the carbon-containing material in a.o. carbon dioxide `CO_2`

Some sorts of rotting go without oxygen, and then methane `CH_4` (a.o.) is produced. Cattle seem to be the main source.

These are called the main greenhouse gases. Carbon dioxide can be re-used by plants for photosynthesis.