# changing the limits of integration in a define integral

When using substitution I understand that the limits of integration need to be changed to fit the substitution.

But can not I use substitution and solve for indefinite integral and in the end use the original limits of integration?

Not sure I understand what you mean. Take $$\int_1^2 x dx =3/2\ .$$ Now set $x=y^2$. So $dx=2y dy$. The indefinite integral in $y$ reads $$\int dy (2y^3)=y^4/2\ .$$ If you compute it between the original limits $1,2$ [without reverting back to $x$] you get $2^4/2-1^4/2=15/2$, which clearly is incorrect.
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