Can I get the integral formula using Matlab?

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Haya M 2021-4-24

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I have the following integration:

$\int_{0}^{2\pi}\frac{1}{\pi}\sin(nx/2)(\pi-x)^2\sin(mx/2)dx$

and m and n are integers.

Can I get the formula for this integration using Matlab?

Here is my attempt:

clear all
syms x m n 
f = (1/pi)*sin(n*x/2)*(pi-x)^2*sin(m*x/2);
Fint = int(f,x,[0 2*pi]);

I got this long result which is ok for me in case it is correct:

(5734161139222659*(8*m^3*cos(pi*m)*sin(pi*n) - 8*n^3*cos(pi*n)*sin(pi*m) - 8*pi*m*n^3 + 8*pi*m^3*n + 4*m^4*pi*sin(pi*m)*sin(pi*n) - 4*n^4*pi*sin(pi*m)*sin(pi*n) + 24*m*n^2*cos(pi*m)*sin(pi*n) - 24*m^2*n*cos(pi*n)*sin(pi*m) - m^5*pi^2*cos(pi*m)*sin(pi*n) + n^5*pi^2*cos(pi*n)*sin(pi*m) - m*n^4*pi^2*cos(pi*m)*sin(pi*n) + m^4*n*pi^2*cos(pi*n)*sin(pi*m) - 2*m^2*n^3*pi^2*cos(pi*n)*sin(pi*m) + 2*m^3*n^2*pi^2*cos(pi*m)*sin(pi*n) - 8*m*n^3*pi*cos(pi*m)*cos(pi*n) + 8*m^3*n*pi*cos(pi*m)*cos(pi*n)))/(9007199254740992*(m^2 - n^2)^3)

when I assume