Would you be able to check my working out of Bn & An for increased time range
3t+3, -2<t<0
t+3, 0<t<2
6t-2, 2<t<6

I get for An
n= 1 (-16/pi^2)
=2 0
=3 (-16/9pi^2)
=4 0
=5 (-16/15pi^2)
=6 0

This look correct for me, the Bn doesn't look right to me

n=1 8(6+1/pi)
=2 48-(4/pi)
=3 48+(8/3pi)
=4 48-(2/pi)
=5 48+(8/5pi)
=6 48-(4/3pi)

you home version of wolfram alpha is something i must get, typing it into the free online one is a pain in the bum.