Question: Numerical Integration without knowing the functional form of the integrand

Let us consider the simple single-variable function,y=f(x)=x*x(i,e,x^2).Now suppose that we don't know our func is x*x,instead we are given:

                                x                                       f(x)

                               -10.0                                  100.0

                              ........                                 ...........

                                0.0                                     0.0

                                1.0                                     1.0

                                2.0                                     4.0

                               .......                                 .........

                                10.0                                  100.0

Now how can I integrate this tabular function numerically in the interval [0.5...9.1]?I also need the plot of the resulting function from integration.

Condition:I can't use any curve fitting method to find the functional form of the tabular data.

Note that I don't have the value of the function at x=0.5 and x=9.1.

Is it possible?

If possible,I need the complete code,a worksheet would be very good.

Thanks in advance.