Summation symbol bound problem

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I am an electrical and electronics engineering student and I am studying signal and systems. We use summation symbol a lot in convolution etc and I am having trouble with my book. In the book it says

the problem on book here

it makes the substitution $k = -m$ but in equation(3.62) summation symbol bounds(upper and lower) are not changed. Should not upper bound be $ -\infty $and lower bound be $\infty$. Can you explain please