We want to find the integral of a function at an arbitrary location x from the origin. Thus,

where I(x=0) is the value of the integral for all times less than 0. (Essentially, I(x=0) is the unknown constant of integration or the initial condition.) From the class lecture on the trapezoidal rule for numerical integration, it can be seen that this function can be approximated by

Write a Matlab function to perform numerical integration of a set of evenly spaced data points using the trapezoidal rule. Your function should accept two vectors as inputs, x and f.

The first vector (x) contains the independent variable data (the points at which the values of the function are known. The second vector (f) should contain the values of the function at the points provided in the first vector. Your function should return the integral of f with respect to x, as a function of x.