integral of f(x), where f(x) is infinite at one point while zero at other parts A function f(x) has the value of zero expect one point, where the value is infinite.  Does the integral of f(x) equal 0? Or any other values? Thanks a lot.

Assuming that you're talking about Lebesgue integration (since we cannot take the Riemann integral of an unbounded function), then the integral is $0$. This is because the function is equal to the zero function except at a single point, and a singleton is a set of measure $0$, so we ignore what happens there.
Now, for example, the Dirac delta function can be loosely thought of as a function that is zero everywhere on the real line, except at $0,$ where it is infinite, and has an integral over the whole real line of $1,$ but again, this is just a rough idea. It is more accurately defined as a measure/probability distribution.
