The curve tool is great for a few things. I am going to show you how to use the autocrop feature of the curve tool.
The curve tool is under the very first tab in the nodes panel in the image section. You can always hit Tab and type curves and it will come up.
What the autocrop feature does is it looks for an alpha then crops your bounding box to fit the alpha channel. This can save some time in render and just over all workflow.
Below is the same image but its alpha channel and bounding box.
Alpha Channel
I hook up the curve tool to the node I want it to analyze and under the curve type I change it to auto crop then click go!
Once it is done analyze you will get a data set under the AutoCropData tab.
Now all you have to do is add a crop node and hold command/ctl and click the animation menu from the curves animation menu to the crop animation menu.
Here is our new bounding box! Now instead of reading a 4k or 2k plate for the whole image it will only update what is in the bounding box!
Here is what my end result nodes look like.
This trick can save you a lot of time when using large images. Sometime it can also take a while to analyze so you have to figure out if the analyze wait is worth the end result.