I’ve created the issue and started to work on merging the 1D integrator into the language, but I think there may be things we need to fix first.

Here’s the issue and the integrator in stan-dev/math.

The doc is a little unclear on types and the type names don’t match in the tparam, but that’s not a big deal.

#### Issue 1

Shouldn’t there be a data argument for real parameters to the function that aren’t differentiated? And shouldn’t there be a data argument for integer parameters? As is, we’ll have to promote real constants and won’t be able to use integer constants from the program.

I think we want this signature for the function that gets integrated, where `theta`

is a parameter vector, `x_r`

and `x_i`

are real and integer data, and `y`

is the variable being integrated:

```
real
f(real y, vector theta, real[] x_r, int[] x_i)
```

Then the function would look like this, where all the variables mean the same thing as above, and `lb`

and `ub`

anre the integration bounds and `abs_tol`

and `rel_tol`

are integration tolerances.

```
real
integrate_definite(F f, real lb, real ub,
vector theta, real[] x_r, int[] x_i,
real abs_tol, real rel_tol)
```

#### Issue 2

Shouldn’t the `vector`

type for `theta`

be `real[]`

instead? That’s what we did with the other integrators.

#### Issue 3

Was there a way to use this to do unbounded integrals with transforms or should I just document the straight-ahead definite integral usage for the manual?