Is the " an integrated approach and teaching vocabulary to English learners " a general topic , for writing essay ?

O.K., because you have "and" between "an integrated approach" and "teaching vocabulary to English learners," you list two *very* general, broad topics, both of which by themselves are much too general, I think, for a single essay.
Maybe you meant to write "an integrated approach to teaching vocabulary to English learners" or "an integrated approach for teaching vocabulary to English learners," using either the preposition "to" or the preposition "for" to head the prepositional-phrase complement of "approach." Either choice would be a good way to limit your topic to make it less general and more appropriate for a single essay, and also grammatically either preposition fits because the next word, "teaching," is already in the gerund form of the verb "teach" which is required after prepositions.
There is a slight difference in the meanings of "approach to teaching" and "approach for teaching," however. If you use "to," the implication is that you may not yet have decided on how to deploy the approach yet but may be considering the approach more theoretically, whereas "approach for teaching" implies that you have decided on a definite approach and will describe it in detail in your essay. So choose which preposition to use based on what your own essay is really about.

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