Step 1: Electric charge passing through the conductor
We know, Instantneous current across a conductor can be defined as:
I=dQdt
⇒dQ=Idt
⇒dQ=(2t+3t2)dt ....(1)
Step 2: Integrate the above equation
Electric Charge flowing through section of the conductor during t=2s to t=3s can be obtained by integrating the equation (1)
∫dQ=∫t=3st=2s(2t+3t2)dt
⇒ΔQ=2[t22]32+3[t33]32
⇒ΔQ=[9−4]+[27−8]=24C
Hence, Option B is correct