**updated:**

with(CurveFitting);

f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3],[4, x4]], x);

f2 := solve(f=y,x);

area1 := int(f, x=0..1);

with(student):

area2 := trapezoid(f2[1], x = 0..1);

with(CurveFitting);

f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3]], x);

f2 := solve(f=y,x);

area1 := int(f, x=0..1);

with(student):

area2 := trapezoid(f2[1], x = 0..1);

i use 5 points trapezoid got RootOf in result,

only 4 points is acceptable

when i try 5 points, there is no problem, but when more points such as

30 points, got RootOf for c sharp code

moreover, i got a problem when i copy the area1 result into

visual studio c# code, it has error Integral Constant is too large

with(CurveFitting);

f := PolynomialInterpolation([[0, x0],[1, x1],[2, x2],[3, x3],[4, x4],[5, x5],[6, x6],[7, x7],[8, x8],[9, x9],[10, x10],[11, x11],[12, x12],[13, x13],[14, x14],[15, x15],[16, x16],[17, x17],[18, x18],[19, x19],[20, x20],[21, x21],[22, x22],[23, x23],[24, x24],[25, x25],[26, x26],[27, x27],[28, x28],[29, x29]], x);

f2 := solve(f=y,x);

area1 := int(f, y=0..1);

with(student):

area2 := trapezoid(f2[1], x = 0..1);

with(CodeGeneration):

CSharp(area1, resultname = "area1");

CSharp(area2, resultname = "area2");

i find area2 has

Warning, the function names {RootOf, Sum} are not recognized in the target language

Warning, precedence for Range unspecified

Warning, cannot translate range

area2 = RootOf((System.Double) (19276689540529530246975515949293568 * x3 - 2626509155780373903082144116707328 * x2 + 239680950855919251544490932629504 * x1 -