  We find the effective action for any D-brane in a general bosonic background
of supergravity. The results are explicit in component fields up to second
order in the fermions and are obtained in a covariant manner. No interaction
terms between fermions and the field $f=b+F$, characteristic of the bosonic
actions, are considered. These are reserved for future work. In order to obtain
the actions, we reduce directly from the M2-brane world-volume action to the
D2-brane world-volume action. Then, by means of T-duality, we obtain the other
Dp-brane actions. The resulting Dp-brane actions can be written in a single
compact and elegant expression.
