Sum data based on buckets/edges (SumIF?)

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I have a data array containing two columns:

Damage value - corresponding to how much damage occurs at that data point

# cycles - how many cycles occur during the data point

I would like to sum the # of cycles for a given set of bins/edges (not always equally spaced). In Excel this would be a very simple SumIF, albeit across a number of cells to populate a table. I can write the same logic in Matlab, but it requires a loop to check each bin/edge set. Is there an elegant single-line solution, similar to histcounts, that will allow me to pass a series of bins/edges and sum the cells that meet that criteria?

In the attached image, the example input data is on the left and the output data I desire is on the right with the thick border around the cells.

Thanks in advance for your assistance!