The previous post in this series presented a User Defined Function (UDF) to fit  a cubic spline to a series of points defined by XY coordinates.  Each segment of the resulting spline is defined by a separate cubic curve, which may be easily integrated to find the area under the curve.  The UDF CSArea() has been added to the cubic spline spreadsheet to perform this function.  The spreadsheet may be downloaded from: CSpline2.zip  As usual, the spreadsheet includes full open source code. 

The screenshot below provides additional detail of the area calculation, and an example finding the area of a semi-circle: 

CSArea Function example, Click for full size view