**Bug introduced in 10.2.0 or earlier and fixed in 10.4.0**


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   Consider the following code.

    ClearAll["Global`*"]
    InactSum = Inactive[Sum]
    InactInt = Inactive[Integrate]
    A = InactInt[
        Subscript[\[Phi], j][x] InactSum[
        Subscript[a, i] Subscript[\[Phi], i][x], {i, 1, n}] , {x, a, b}]
    B = InactInt[
        InactSum[Subscript[a, i]
        Subscript[\[Phi], i][x] Subscript[\[Phi], j][x], {i, 1, n}] , {x,
        a, b}]
    Interchange = InactInt[InactSum[p_, q_], r_] -> InactSum[InactInt[p, r], q];
    A /. Interchange
    B /. Interchange

I have introduced two expressions 

$$\begin{align}
A &= \int_{a}^{b} \phi_{j}(x) \left[ \sum_{i=1}^{n} a_i \phi_{i}(x) \right] dx \\
B &= \int_{a}^{b} \left[ \sum_{i=1}^{n} a_i \phi_{i}(x) \phi_{j}(x)\right] dx
\end{align}$$

where in $A$, $\phi_{j}$ is outside the summation while in $B$ it is inside the summation. Technically, these are both the same. But when I was trying to write a transformation rule that interchanges the integration and summation, then I noticed that it just applies to $B$ and **not** to $A$. So, I understood that Mathematica understands the **little** difference between these two but

**The Standard Output for Both is the Same!**

[![enter image description here][1]][1]

This prevents user from understanding the difference and it just shows itself when you want to apply the transformation rule.

I think this is a bug. In my opinion, the standard output for these two should be different. I would be happy to see what you think.


  [1]: https://i.sstatic.net/XGR0g.png