SplineIntegrate.txt

The indefinite integral of y = a x^3 + b x^2 + c x + d
        is           inty(x) = a/4 x^4 + b/3 x^3 + c/2 x^2 + d x
        
The definite integral from x=xa to x = xb
        is           inty(xb) - inty(xa)
        
Given the Spline fit coefficients ai, bi, ci, di  i=1..n-1

Case 1 The  x values are equally spaced and xa=x1 and xb=xn

   h = xi+1 - xi
   integral = h^4/4 sum(ai) + h^3/3 sum(bi) + h^2/2 sum(ci) + h sum(di) 
   where sum is i=1..n-1
   
Case 2 The  x values are not equally spaced.

   hi = xi+1 - xi
   integral = sum(hi^4/4 ai + hi^3/3 bi + hi^2/2 ci + hi di)
   where sum is i=1..n-1   

Use Horner's method to evaluate polynomials