Let \([x]\) denote the greatest integer function. Then \({\int }_{−\frac{\pi }{2}}^{\frac{\pi }{2}}\left(\frac{12\text{ …

Let \([x]\) denote the greatest integer function. Then \({\int }_{−\frac{\pi }{2}}^{\frac{\pi }{2}}\left(\frac{12\text{ }\left(3+\left[x\right]\right)}{3\text{ }+\text{ }\left[\sin \text{ }x\right]\text{ }+\text{ }\left[\cos \text{ }x\right]}\right)\text{ }dx\) is equal to:

[JEE Main 2026, 28 Jan (Shift 2)]