The official source for Maharashtra State Board textbooks is eBalbharati.

Theorem proofs (like the properties of definite integrals) are often asked directly in the 3-mark or 4-mark question sections.

Mathematics Standard Stage 6 Syllabus (2017) - NSW Government

One of the best things about these resources is that the provides official textbooks for free. Here are the most common and reliable ways to download your copy:

Continuity, differentiability, derivatives of composite functions, inverse trigonometric functions, and implicit functions.

Various state education boards provide free digital versions of their textbooks on their official websites (e.g., Mahahsscboard.in).