This page contains some programs for integrating and differentiating numerical data. A function $f(x)$ is can be specified either by inputting a formula at the top or by pasting two columns of data in the textbox at the top-left. When the "calculate from formula" button is pressed, the formula is used to fill the table with 1000 equally spaced values of $f(x)$ equally spaced between $x_1$ and $x_2$. When the "calculate from table" button is pressed, the data is plotted on the right. Below the data and plot of $f(x)$, the derivative $\frac{df}{dx}$ and the second derivative $\frac{d^2f}{dx^2}$ are tabulated and plotted. Below the derivatives, the integral of $f(x)$ is shown as well as the integral of the integral. The integration routines assume that the measurements are equally spaced with an interval $\Delta x$.

If the data points you have are not equally spaced in $x$, you can use either of the apps linear interpolation, or cubic spline to generate data points that are equally spaced in $x$.