I do not have Maple 8 at hand, but the issue seems to be related to the structure of the result returned by both functions. Spline returns a piecewise function, whereas BSplineCurve returns a parametric function. So the first structure can be directly integrated. Here is what we can read in Maple 11 online help for Spline,

The Spline routine computes a degree d piecewise polynomial in variable v that approximates the points {(x0, y0), (x1, y1), ..., (xn, yn)}.

and for BSplineCurve,

The resulting curve is in parametric form [xf(v), yf(v), v=a..b], where xf(v) and yf(v) are piecewise functions of v, and a..b is the range over which the B-spline curve is defined.

with(CurveFitting):
Spline([[0,0],[1,1],[2,4],[3,3]], v);

                /       1     4  3         14   41     42  2      3  
       piecewise|v < 1, - v + - v , v < 2, -- - -- v + -- v  - 2 v , 
                \       5     5            5    5      5             

           114   151     54  2   6  3\
         - --- + --- v - -- v  + - v |
            5     5      5       5   /

type(%, piecewise);
                                    true

Does this match your problem with Maple 8?

Regards,
--
Jean-Marc

The output of BSplineCurve is in parametric form [x(t), y(t), t=a..b]. If by "integrate the output" you mean you want , that would be

Thus:

> C:= BSplineCurve(..., t);
  int(C[2]*diff(C[1],t), C[3]);