Show integral(a,b)(f(x+c)dx = integral(a+c,b+c)(f(x) dx.

Let u = x+c, then du = dx so integral(a,b)(f(x+c)dx = integral(a+c,b+c)f(u)du. But when I substitute u back in, I get integral(a+c,b+c)(f(x+c)(du) which does not equal integral(a+c,b+c)(f(x)dx. What am I doing wrong?