JEE Advanced 2023 Mathematics question on Definite Integrals and Areas

1. A.
   There exists an $h \in \left[\dfrac{1}{4}, \dfrac{2}{3}\right]$ such that the area of the green region above the line $L_h$ equals the area of the green region below the line $L_h$
2. B.
   There exists an $h \in \left[\dfrac{1}{4}, \dfrac{2}{3}\right]$ such that the area of the red region above the line $L_h$ equals the area of the red region below the line $L_h$
3. C.
   There exists an $h \in \left[\dfrac{1}{4}, \dfrac{2}{3}\right]$ such that the area of the green region above the line $L_h$ equals the area of the red region below the line $L_h$
4. D.
   There exists an $h \in \left[\dfrac{1}{4}, \dfrac{2}{3}\right]$ such that the area of the red region above the line $L_h$ equals the area of the green region below the line $L_h$

[JEE Advanced 2023 · Paper 1]