How is this integral related to the variance or cdf.

Hello

I feel like this is a bit of a stupid question, but I guess worth asking.

I have come across the integral,

$\displaystyle \int _{-\infty }^x(t-\mu )^2f(t)dt$

where $\displaystyle f(x)$ is a probability density function. This looks kind of familiar! I can't compute this integral analytically. I do however know what the variance is. I was wondering how this integral is related to the cdf or the variance. Maybe its too much of an ask but I was hoping by being able to relate this integral to some known quantity I may be able to evaluate it.

Thanks for reading