How doubling the mean affects area under the curve for normal distribution

This is mcq type question which says, 'For a normal distribution, if the mean is doubled, how does the area under the curve change?'
Options were

1. Remains same
2. Halves
3. Doubles
4. Need standard deviation to estimate area

I think option 4 should be correct as we need both mean and standard deviation to estimate area. But not sure about it.

The definition of "curve" in the problem appears vague, but area under the probability distribution curve is always 1 (by definition), independent of the mean and standard deviation.

$f(x) = {1 \over \sigma \sqrt{2 \pi}} \exp{-(x-\mu)^2 \over 2 \sigma^2}$, where $\mu$ is the mean and $\sigma$ is the std dev of the distribution

Area under the curve: $\int_{-\infty}^\infty f(x)dx = 1$