Good question; indeed, both appear correct, and from this quote alone it may be rather difficult to ascertain the proper answer (although many may say instinctively that dropping the article is best). I believe the answer, though, lies in the context built prior to the quote itself, and relies on your insight as to a "specific entity."
If the text explains explicitly "political life" prior to this statement, such as imparting to the reader both tasks and importance of involvement, then it could be assumed that "political life" is now specific enough to both reader and writer to be considered a definite reference, and thus "the" would be appropriate. However, if "political life" is discussed in a more abstract sense, leaning towards expressing its complexity through broad statements (or even just assumed to be understood in the piece), it would be best to drop "the" as the idea of "political life" is now an indefinite reference.
I would bet that in this case, as test appears to be a broad history book, that "political life" acts as more of a broad term covering many facets of societies throughout the ages, thus falls in the latter category of an indefinite reference, and is best without using "the."
To read more on definite/indefinite references, I found a great resource from CUNY School of Law here.
Hope this helps!