So how do you do it?
Here is the idea. We create a spreadsheet, in one column of which we start with the lower limit of integration and increase values of the argument by some amount, d, per row. This can be arranged by one or two entries and copying down. You can call this the argument column.
In the next column, we evaluate the integrand at each argument. This can be done by evaluating it at the first entry, and copying down. This can be called the value column for your integrand.
In the final row we sum the entries in the previous column, each multiplied by d, This again requires one entry and copying down. And that is essentially it. This is the integral column. Its entry is the integral from the beginning point to the next entry in the argument column, using the "left hand rule".
Before fleshing this out in detail, we will digress to discuss,"rules" to use for the numerical integration.