When calculating the integral of two orthogonal sine functions

sin (n Pi x) sin (m Pi x), n, m integers> 0

Mathematica seems to lose the solution where n = m. I don't understand exactly why this is lost. It is possible to find the solution by taking the limit of the expression it gives; In the following example, this is found by taking the limit as n_> 5.

Have I coded something incorrectly?

Thank you.

Sample Code

```
(* compute the integral of two orthogonal sine functions *)
a =
Integrate(Sin(5 Pi x) Sin(n Pi x), {x, 0, 1},
Assumptions -> {n (Element) Integers && x (Element) Reals &&
m (Element) Integers && n > 0 && m > 0})
(* Simplify the result *)
B(n_) = FullSimplify(a,
Assumptions -> {n (Element) Integers && x (Element) Reals &&
m (Element) Integers && n > 0 && m > 0})
Out(31)= (5 Sin(n (Pi)))/(25 (Pi) - n^2 (Pi))
Out(32)= 0
(* Apparently, FullSimplify misses the case where n=5. Zero is correct only when n≠5 *)
(*Taking the appropriate limit of the function before FullSimplify yields the correct result *)
In(30):= Limit((10 Sin(n (Pi)))/(25 (Pi) - n^2 (Pi)), n -> 5)
Out(30)= 1/2
```