$\forall xP(x) \vee \exists yP(y)$ is true
$\implies$ either $\forall xP(x)$ is true or $\exists yP(y)$ is true …..$(i)$
Now, if $P(x)$ is true for all $x$ then $P(x)$ will be true for some $x$ also right ?
i.e. $\exists xP(x)$ is true , put this in eq $(i)$
$\implies$ either $\exists xP(x)$ is true or $\exists yP(y)$ is true
$\implies \exists xP(x) \vee \exists yP(y)$ is true
write $x$ in place of $y$
$\implies \exists xP(x) \vee \exists xP(x)$ is true
$\implies \exists xP(x) $ is true
$\therefore$ Option A is correct.