****** -2 to 0 part ****** A

start:
1/2 * INTEGRAL(-2, 0, 2 * sin(n*pi*x/2), dx)

integrate:
1/2 * (-4/(n*pi) * cos(n*pi*x/2)) ] (-2,0)

evaluate:
-2/(n*pi) + 2/(n*pi) * cos(n*pi)



 ****** 0 to 2 first part ****** B

start:
1/2 * INTEGRAL(0, 2, 2 * sin(n*pi*x/2), dx)

integrate:
1/2 * (-4/(n*pi) * cos(n*pi*x/2)) ] (0,2)

evaluate:
1/2 * (-4/(n*pi) * cos(n*pi) + 4/(n*pi))
-2/(n*pi) + 2/(n*pi) * cos(n*pi)



 ****** 0 to 2 second part ****** C

start:
1/2 * INTEGRAL(0, 2, x * sin(n*pi*x/2), dx)

integration by parts:
u = x
du = 1
v = -2/(n*pi) * cos(n*pi*x/2)
dv = sin(n*pi*x/2)

v*u - INTEGRAL(v*du)
1/2 * (-2*x/(n*pi) * cos(n*pi*x/2) - INTEGRAL(-2/(n*pi) * cos(n*pi*x/2)) ] (0,2))
1/2 * (-2*x/(n*pi) * cos(n*pi*x/2) + 4/(n^2 * pi^2) * sin(n*pi*x/2) ] (0,2))

evaluate:
1/2 * ( (-4/(n*pi) * cos(n*pi) + 4/(n^2 * pi^2) * sin(n*pi)) - (-2*0/(n*pi) * cos(n*pi*0/2) + 4/(n^2 * pi^2) * sin(n*pi*0/2)) )
1/2 * ( (-4/(n*pi) * cos(n*pi) + 4/(n^2 * pi^2) * sin(n*pi)) - (-0 * cos(0) + 4/(n^2 * pi^2) * sin(0)) )
1/2 * ( (-4/(n*pi) * cos(n*pi) + 0) - (0 + 0) )
1/2 * ( -4/(n*pi) * cos(n*pi) )
-2/(n*pi) * cos(n*pi)



FINAL EQUATION:
A + B - C
-2/(n*pi) + 2/(n*pi) * cos(n*pi)   +   -2/(n*pi) + 2/(n*pi) * cos(n*pi)   -   -2/(n*pi) * cos(n*pi)