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Does the area under the graph means anything?

In the analysis page, does the area under the advantage graph means anything mathematically?

A question for the mathematicians out here :P
If you were to take the integral of the entire chart then you would get the rate of change of the advantage of the entire game. If it is positive then that means white had the advantage more often and vise versa. It would be an interesting unit of measure for determining who played better generally throughout the game.
It wouldn't mean much, since the area will be mostly proportional to the lenght of the game (in number of moves) than anything else, giving then only a relative (to the other player) measure of the advantage sustained through more or less number of moves by with no strict relation of how the game ended (something like average centipawn loss). In a long game, or a game with advantage reversed at the end, this number would be pretty much useless since the number itself can't give a clear picture of how a game was. MUCH MORE useless would it be to compare anything to other games.
Maybe combining this integral with another parameter, an intersting number can arise but i can't thing of any right now. I'm not a mathematician, by the way.

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