This morning I read a post at sage-devel group titled “Integral Functions”, and was really interesting.
For example, say you want to define a function as the primitive integral of another function,
sage: var('x')
sage: f = function('f',x)
sage: F = integral(f, x, 0, x)
sage: F.derivative(x)
gives an error… Why? derivative expect all parameters of 
Bypass
A sort of solution to this problem is giving a whole set of parameters to the limits, say,
sage: var('x,a,b')
(x, a, b)
sage: f = function('f',x)
sage: F = integral(f, x, a, b)
sage: F.derivative(x)
0
sage: F.derivative(a)
-f(a)
sage: F.derivative(b)
f(b)
Thus, it’s well defined for any case.
If you don’t give integration limits,
sage: var('x')
sage: f = function('f',x)
sage: F = integral(f, x)
sage: F.derivative(x)
f(x)
it work as expected.
The discussion page is HERE
Enjoy!
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