Comment #17 on issue 2571 by [email protected]: Regression in Integral.subs
http://code.google.com/p/sympy/issues/detail?id=2571

Why not just do

i = my_integral
inew = i.func(i.function.subs(old, new), i.limits)

Otherwise you have to come up with an acceptable criteria to govern the
rules of the substitution...and the more rules you have the harder it is to
foresee what the substitution will be. Right now, there is one rule:
substitutions on integrals can replace anything that isn't locked down by
an integration variable.

Besides the simple example in the issue (replacing x with 5 in Integral(x,
x)) here is another scenario: for Integral(x, (x, x**2)).subs(x, y) what
should the answer be:

y**3

x**2*y

y**4/2

/c

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