Let f(X) be an indefinite integral of sin²x.
Statement I: The function F(x) satisfies $\mathrm{F}(\mathrm{x}+\mathrm{\pi })=\mathrm{F}\left(\mathrm{x}\right)$ for all real x
Statement II: ${\sin }^2(\mathrm{x}+\mathrm{\pi })={\sin }^2 \mathrm{x}$ for all real x.

Statement I is true, Statement II is also true; Statement II is the correct explanation of Statement I

Statement I is true, Statement II is also true; Statement II is not the correct explanation of Statement I

Statement I is true; Statement II is false

Statement I is false; Statement II is true