Is this a bug in IntegrateChangeVariables?

Question

Bug introduced in 13.1, persisting through 13.2.1.

---

h[i_] = i^(-11./10);
d = 50;
eval[int_] := Print["Value=", N[Activate[int] /. s -> d]];
int = Inactive[Integrate][Exp[-s h[i]]/d, {i, 1, d}];
eval@int;
int = IntegrateChangeVariables[int, hi, hi == h[i]];
eval@int;

It prints

Value=0.230237
Value=-0.00252577

I could work around the other bug by negating the result, but this one seems more serious.

Manual change of variables works with some warnings

gi[y_] = First@SolveValues[h[x] == y, x];
arg = -D[gi[y], y]*Exp[-s y]/d;
Integrate[arg /. s -> d, {y, h[d], h[1]}]    (* 0.230237 *)

Answer 1

The wrong integral region is caused by failure of convergence of NMinValue.

MinValue[{x,1.<=1./x^(10/11.)<=50.&&x∈Reals},x]

To bypass it, change the method e.g.

SetOptions[MinValue,Method->"SimulatedAnnealing"]

then

h[i_] = i^(-11./10);
d = 50;
eval[int_] := Print["Value=", N[Activate[int] /. s -> d]];
int = Inactive[Integrate][Exp[-s h[i]]/d, {i, 1, d}];
eval@int;
int = IntegrateChangeVariables[int, hi, hi == h[i]];
eval@int;

---

Some of the Messages are suppressed by default. To locate the bug we can use trick like

Block[{Quiet=#&},
  On[General::stop];
  your code here
]

and then see if some errors have been hidden...