Find monthly totals from (occasional) daily entries

I'm fully expecting a 'read page one of chapter xyz' reply because this seems to be something that should be trivial but I can't work it out.

How do I derive a list of monthly totals from a list of daily readings?

From

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to

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So find the month of the first entry. Find the month of the last entry. For each month in this range find the first and last entries (and the last entry of the previous month and the first entry of the next month). Extrapolate between first of this month and last of previous month to get reading for 1 of month then do similar for last. Etc.

BUT before I sit down to hack at that I thought this is such an obvious requirement that there must be a built-in way to do this semi-automatically and I'm being stupid. But I can't find it. Is there?