Prove that if $f,g:S^1\to X$ are homotopic maps, then the spaces formed from $X$ by attaching a disc using $f$ and using $g$ are homotopy equivalent

Question

Prove that if $f,g:S^1\to X$ are homotopic maps, then the spaces formed from $X$ by attaching a disc using $f$ and using $g$ are homotopy equivalent; in other words, $X\cup_f D\simeq X\cup_g D$.

I have no idea about it.

It is an exercise from M.A.Armstrong, Basic Topology, so the answer shouldn't be complex.