If there four options are given to a Defenite Integration then what shortcut trick we should choose to get the correct answer.

Like in Indefinte Integration we find the differtation of the answer to reach the function given to integrate.

You can try to eliminate some answers as follows.

|int f(x)dx| <= int |f(x)|dx <=
max[f(x)]*(length on the integration interval).

Options that are inconsistent with this inequality can be eliminated.