How can I get undefined unevaluated integrals to be treated like number?

Question

I am working with commutators like this $$ \left(a \int f \, \mathrm dt\right) * a - a * \left(a \int f \, \mathrm dt\right),$$

comm[A_, B_] := ExpandAll[A ** B - B ** A //. a ** ad :> ad ** a + 1]
comm[-a Integrate[f[1, t], t], a ** a]

where $a$ is a ladder operator, and I would like the integral to be treated like a number and factored out. For some reason, this expression isn't simplifying to zero.

I tried

Integrate /: NumberQ[Integrate[expr_]] = True;

which doesn't seem to help, and also

Integrate /: NumberQ[Integrate[expr__]] = True;

and

Integrate /: NumberQ[Integrate[__]] = True;

seem to be working but both give the error

Integrate called with 1 argument; 2 or more arguments are expected.

What is the correct syntax for this command?

Note that I also use a variety of rules such as

A_ ** (B_ + C_) := A ** B + A ** C

Answer 1

Suppress evaluation at all instances

  SetAttributes[comm, HoldAll];
  comm[A_, B_] := A ** B - B ** A -> 
    ReleaseHold[ExpandAll[Hold[A ** B - B ** A] /. {HoldPattern[a ** ad_] :> ad ** a + 1}]]


    comm[-a Integrate[f[1, t], t], a ** a]

$$(-a \int f(1,t) \, dt)\text{**}a\text{**}a-a\text{**}a\text{**}(-a \int f(1,t) \, dt)\to (-a \int f(1,t) \, dt)\text{**}(a\text{**}a+1)-(a\text{**}a+1)\text{**}(-a \int f(1,t) \, dt)$$