Please, for your next question: Always post WHOLE sentences, not fragments. Grammar is the science of joining words together to form sentences, not fragments!
Your fragment seams to be a subordinate clause. Maybe the full sentence was something like this:
Lisas Aufgabe war, die heiligen Bücher von Indien mit heim nach China zu bringen.
Lisa's task was to bring the holy books along from India home to China.
Without »heim nach China« (home to China) it would be this sentence:
Lisas Aufgabe war, die heiligen Bücher von Indien mitzubringen.
Lisa's task was to bring the holy books along from India.
The same verb in a main clause:
Lisa bringt die heiligen Bücher von Indien mit.
Lisa brings along the holy books from India.
Futur I (becasue in this tense, the verb is used in its infinite form:
Lisa wird die heiligen Bücher von Indien mitbringen.
Lisa will bring along the holy books from India.
The German verb etwas mitbringen means
- to bring something along
- to bring something with one
The prefix mit- always means, that something happens together with something else (German preposition mit = with). So, mitbringen means, that Lisa travels from India to China, and together with (mit) this movement she brings something from India to China.
You could also use just bringen = to bring, but there is a very subtile difference:
- Tom wird die Pizza zur Party bringen.
- Tom wird die Pizza zur Party mitbringen.
Both sentences mean "Tom will bring the pizza to the party". But in #1 it is very likely, that Tom is just the pizza delivery boy. He rings, delivers the pizza and then drives back to where he came from. In sentence #2 it is very clear, that Tom is one of the guests. He is coming because he wants to attend the party. Bringing the pizza is just the subplot.
The same is true for the person who brings the books from India to China. If you use bringen (without mit-) then the most likely meaning is, that this person acts like the pizza boy: The purpose of the travel is to deliver the book. When this is done, the person travels home to India.
But when you use mitbringen, then you say, that the person is traveling to China anyway, for some other reason. And because this person is by accident on the way to China, and the books needs to be brought there, is is a good idea, that this person brings them. But the main reason for the journey is not bringing the books, but something else.
You also already have noticed, that mitbringen is a separable verb. They split and merge depending on the grammatical context:
- Futur I
Er wird etwas mitbringen.
Er bringt etwas mit.
- Perfekt (here you need the participle)
Er hat etwas mitgebracht.
- »Erweiterter Infinitiv« or »Infinitiv mit "zu"«
Er beschließt, etwas mitzubringen.
So, mitzubringen should be written as one word. But only becasue it is a separable verb. Bringen is not separable, so when you use just bringen (without "mit"), the correct version is
Er beschließt, etwas zu bringen.
And now comes the trick:
You can squeeze other parts of speech between the parts of a separable verb. But when you do so, you obviously are no longer able to write the parts together as one word. And then, you have to separate al three parts:
... mitzubringen → ... mit ... zu bringen
- Lisas Aufgabe war, die heiligen Bücher von Indien mitzubringen.
- Lisas Aufgabe war, die heiligen Bücher von Indien heim nach China mitzubringen.
- Lisas Aufgabe war, die heiligen Bücher von Indien mit heim nach China zu bringen.
Versions 2 and 3 are both correct. It is just a matter of personal flavor which of them you prefer.