How to calculate the variance of a continuous distribution function but with a mass point?

Question

I have a continuous distribution function, but it has a mass point at the upper bound, say with a probability of p>0. How to calculate its variance?

Answer 1

If $b$ is the upper bound then the variance is $\int x^{2} f(x)\, dx-(\int f(x) \, dx)^{2}+b^{2}p-bp$ where $f$ is the density up to $b$.