I need to prove:

I(subscript 2k)=integral[-1,1](x^2k)*(cos(pi*x))dx

is equal to

I(subscript 2k)=-(4k/pi^2)-((2k)(2k-1)/(pi^2))*I(subscript 2k-2)

but i keep getting

I(subscript 2k)=-(4k/pi^2)+((2k)(2k-1)/(pi^2))*I(subscript 2k-2)

can anyone help?