In order for it to be truly general, you will need to interpolate the "function". For example, we might do this:
Now, we wish to integrate y, but only based on the values we have generated. Remember that integrating beyond the linits of our data will be bad idea, because then we are forced to extrapolate the function. And THAT is a bad idea, unless our extrapolant is one chosen carefully. A spline will be a terribly poor tool to extrapolate.
Now, assume we wish the integral of y, between x and x + c. In this example, I'll use x=0.1223, and c=4.75.
fintxc = @(x,c) fnval(fint,x+c) - fnval(fint,x);
How well did we do? Remember, this can be no more than an approximation. We can use integral on the original function to do the work, although I could be more intelligent, since I know the integral of the sine function. I'll take the lazy way here.
integral(@sin,0.1223,0.1223 + 4.75)
Which given the coarseness of the original sample, is not at all bad.