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When can the upper limit of definite integral be put forward in advanced mathematics?
It is not "putting forward the upper limit of integral" or "putting forward the factor of upper limit of integral". But:

I =∫& lt; 0,π& gt; (sinx)^4dx =∫& lt; 0,π/2 & gt; (sinx)^4dx+∫& lt; π/2,π& gt; (sinx)^4dx

For the latter, let x = π-u, and we get

I2 =∫& lt; π/2,π& gt; (sinx)^4dx =∫& lt; π/2,0 & gt(sinu)^4(-du)=∫& lt; 0,π/2 & gt; (sinu)^4du

Definite integral has nothing to do with integral variable. If u is replaced by x, I2 = ∫.

Then I = ∫ < 0, π >; (sinx)^4dx = 2∫& lt; 0,π/2 & gt; (sinx)^4dx