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.

It sounds like you are thinking about the Dirac delta "function" which is not a proper function.  Changing the value of a function at one point cannot change its integral.  It is not allowed in $\Bbb R$ to have the value of a function be infinite.  You can explore this term on this site and elsewhere to learn its properties.
