No, not really. The question isn't asking you "prove this method gives the wrong result", it's asking "what is wrong with this method?".
Suppose I ask you "what is wrong with the following argument?":
[indent]Suppose x = y. Then:
x2=xyx2−y2=xy−y2(x+y)(x−y)=y(x−y)(x+y)=y2x=yTaking the particular choice x=y=1, we find 2 = 1.[/indent]
If you say "the argument is wrong because
2=1", you won't get any marks. Instead you would need to say something like "
You can't go from (x+y)(x-y) = y(x-y) to x+y = y, because you're dividing by (x-y) which is zero".
To look at it another way, the question asks "explain why
the substitution x=1/t does not show the integrals are equal" (emphasis mine). So if your explanation doesn't even
mention the substitution x=1/t, then you're in trouble!
In terms of the original question, to understand a bit better what's going on, you might want to consider what happens to
∫01(1+x2)21dx and
∫−10(1+x2)21dxunder the substitution
x=1/t.
This is somewhat belabouring the point for this particular question - I can't think the explanation would be worth many marks, and I'd expect you do get most of them for any explanation mentioning the behaviour of 1/x at x=0.