Integrating a constant. Do we leave a 1 when moving constant?

Question

I need to integrate the following: $\frac{1}{T} \int_{0}^{T}\left(\ln S_{0}\right.)$.

I know that what it should be is: $\ln S_{0}.$

I need to be sure im doing this the right way, so im thinking of doing this:

$\frac{1}{T} \int_{0}^{T}\left(\ln S_{0}\right)$

$=\frac{1}{T} \ln S_{0} \int_{0}^{T} 1$ : take the constant outside, and we are left with 1

$=\frac{1}{T} \ln S_{0} \int_{0}^{T} 1$ : integrate from 0 to T, and we get T

Multiply that T with $\frac{1}{T}$ and we get 1, so the final result is: $\ln S_{0}$

Answer 1

This is correct, except we need to specify what variable you’re integrating with respect to. Answer from Tavish