Why is the integrand bounded on [$0,b$] when integrand can be infinite for $x=0$

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Why is the integrand bounded? The only way I can see that it is bounded is if $x$ never is equal to 0, but if this is true (that $x\neq 0$) then where is this indicated that we don't use the endpoint?

"Open the question so I can answer it as I know the answer to it now"- also I am not sure what to do it open it