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Default Calculating or estimating the area between to curves

I have seen some great posts about colouring the area between 2 lines but I
need to calculate numerically the area between 2 lines. A close estimate
would do. My curves are smoothed lines but they have many roots to fit a
trendline whose equation I could have integrated. If I use straight lines
between points I have too big an error. Even Simpsons Rule is not accurate
enough at times. Is there a way that Excel can return a figure for the area
under a curve - I could even use the number of pixels it has shaded between
the 2 lines!
 
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