Mean and standard deviation of probability density function?

Suppose the probability density function is f(x), defined over a domain D

Then the mean is E(X) = x*f(x) integrated with respect to x over D.

Calculate E(X2) = x2*f(x) integrated with respect to x over D.

Then Variance(X) = E(X2) - [E(X)]2

and Standard Deviation = sqrt(Variance).