Given below are two statements:
Statement I: Area under velocity-time graph gives the distance travelled by the body in a given time.
Statement II: Area under acceleration-time graph is equal to the change in velocity in the given time.
In the light of given statements, choose the correct answer from the options given below.

We need to analyze each statement carefully.

For Statement I, it says the area under the velocity-time graph gives the distance travelled. However, the area under the velocity-time graph actually gives the displacement, not the distance. Distance is the total path length and equals the area only when velocity does not change sign. If velocity becomes negative, the area below the time axis is negative, giving displacement. To get distance, we would need the area under the $$|v|$$ vs $$t$$ graph. So Statement I is incorrect in general.

Now consider Statement II, which says the area under the acceleration-time graph equals the change in velocity. We know that $$a = \frac{dv}{dt}$$, so

$$\int_{t_1}^{t_2} a \, dt = v(t_2) - v(t_1) = \Delta v$$

The area under the acceleration-time graph indeed gives the change in velocity (since integrating acceleration over time recovers the velocity change). So Statement II is true.

Hence, Statement I is incorrect but Statement II is true. Hence, the correct answer is Option 4.