How does a difference under the integral sign turns into a definite integral of just a dummy variable?

Question

I'm trying to follow trhough the proof of a statistics theorem due to Pratt (Full proof here, from Casella-Berger's Statistical Inference, 2nd Ed., p. 447), but I'm stuck with this passage:

$$\int_{\chi}[U(x)-L(x)]f(x|\theta^*)dx=\int_{\chi}\biggl[\int_{L(x)}^{U(x)} d\theta\biggl]f(x|\theta^*)dx$$

How does the difference $U(x)-L(x)$ turns into an integral of just the dummy variable $d\theta$ ?

Thanks in advance.