What exactly does $\left. f(x)+g(x) \right|_{a}^{b}$ mean?

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So we know that

$$\left[ x^2+2x \right]_{a}^{b} = b^2+2b-a^2-2a$$

This is quite clear from the notation. However, there's another fairly common evaluation notation, as follows:

$$\left. x^2+2x \right|_{a}^{b}$$

In this case, it becomes a but confusing. The question then is whether it means $\left[ x^2+2x \right]_{a}^{b}$ or $x^2 + \left[ 2x \right]_{a}^{b}$.

This is quite important when writing things like

$$\left. x^3-4x \right|_{1}^{2} + \left. x^2+2x \right|_{3}^{4}$$

where it's not completely clear if the $3$ and $4$ limits refer to the $x^2+2x$ or just the $2x$. This problem can prop up when integrating by parts or doing some questions.

Which one does it apply to, then? Does the evaluation symbol "$|$" apply to all terms before it, up until the next evaluation symbol on the left?