The limits have not been given and we don’t know what '' means.
However, it is possible to find a solution.
If the integral was ∫x³dx where x in [2,4] , then the definite integral is ¼[x⁴] for x ∊ [2,4].
This evaluates to ¼(4⁴-2⁴)=¼(256-16)=240/4=60, answer b.
The reasoning is this:
For x⁴/4 between limits a and b, we get (b⁴-a⁴)/4=one of the given options. All of the options are even so, a and b are both odd or both even. If they’re both even then a=2n and b=2m where n and m are integers.
So we have (16m⁴-16n⁴)/4=4m⁴-4n⁴={68 60 240 56} where one of the options is the right answer.
Therefore m⁴-n⁴={17 15 60 14}. If n=1, then m⁴={18 16 61 15}. The only one of the options, that is, a number to the power of 4, is 16, which has a 4th root of 2, so m=2. Therefore b=2m=4 and a=2n=2.
This is one solution: ∫x³dx where x in [2,4]=60, answer b.
Now try n=2. m⁴={33 31 76 30}, none of which gives us a number raised to power 4. And n=3 doesn’t give us any solutions either.