Integrating the area above or below the closing price line does not give one insight into how much volume transpired for the given area under the curve. This is not a simple integration problem of solving the area under a curve. Not how it works.
One would need to know the corresponding vol under that curve for it to indicate the net buying or selling taking place. Knowing the daily tick by tick volumes would be difficult to get w/o some very specific trading software. It's likely available but I don't have a program like that. One has to just use the daily chart in general and look for the very large vol "prints" which show up as large vol spikes on the daily chart.
To integrate the area under the area above and below the daily neutral line really won't tell on much of anything significant unless multiplied by the corresponding total volumes for those given areas.
One would integrate say area from "a" to "b" above the line and then multiply by volume "X" positive above the line and then say integrate the area under the volume under the daily neutral line from "c" to "d" and then multiply it by "-y" and get a negative number for under the line total area X vol. One could then subtract using X - Y and see if it's a positive or negative number. That might give some indication of net volume flow above or below the neutral line.
Simply integrating area above or below the daily neutral line is not going to reveal much IMO. W/o vol a key indicator is missing. One has to especially also bring into play things like MM's, what vol was short, the size of vol orders, etc. Net money flow is more or less what one is looking for- was it positive or negative and a simple area integration won't reveal that.
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