What is the name of the part by the right-hand pedal on to which the chain grips? There's a part common to all bikes that resides by the right-hand pedal that holds the front sprockets upon which the chain grips?

I'm aware that this part contains the sprocket or sprockets on to which the chain grips. I'm aware that this part will often contain the right pedal arm.

I'm not aware of the name of the part itself. What is this called?

I'm asking as I have one that is slightly bent. I'm looking for the correct terminology to better find out how one might best return this part to its non-bent state.

The part to which I'm referring look like this:
The entire assembly is called the crankset.

The ring with the teeth is called the chainring.

The crankset consists of the crank arm, the spider and the chainrings.
The chainrings bolt onto the spider which is the multi-armed piece connected to the crank arm. 

The right crank arm and spider are often one piece. Lower-end cranksets are forged or riveted together, while higher-end (like the one shown in the question) are bolted. With bolted cranksets one can exchange only the chainrings; with monolitic ones the whole assembly has to be replaced once the chainrings are worn.