Mathematics

The key insight is that the integral's sign depends on which region contributes more area—the negative part from $(0,2)$ or the positive part from $(2,5)$. Since $h$ is continuous and changes sign at $x=2$, you can split the integral into two pieces and think about their magnitudes. The total integral could be negative, positive, or zero depending on how large each region's area is; without knowing the actual function values, you can't determine a single definite sign—but you can rule out certain claims about what must be true.

The key insight is that the integral's sign depends on which region contributes more area—the negative part from $(0,2)$ or the positive part from $(2,5)$. Since $h$ is continuous and changes sign at $x=2$, you can split the integral into two pieces and think about their magnitudes. The total integral could be negative, positive, or zero depending on how large each region's area is; without knowing the actual function values, you can't determine a single definite sign—but you can rule out certain claims about what must be true.