Math Help - Dirichlet's Kernel in Fourier Analysis

1. Dirichlet's Kernel in Fourier Analysis

Prove that 1/2 $\pi$ $\int$f(t)Dn(x-t)dt = 1/2 $\pi$ $\int$f(x-t)Dn(t)dt
the integral ranges from - $\pi$ to $\pi$

Dn represents the nth Dirichlet's Kernel, $\sum$ e^ikx as k ranges from -n to n
i tried a substitution where u = x - t which yield -du = dt
so the integral i am getting is
1/2 $\pi$ $\int$f(t)Dn(x-t)dt = - 1/2 $\pi$ $\int$f(x-u)Dn(u)du

any help would be welcomed

2. figured out my mistake