Doubt from definite integration

Question no 114 i forgot how to open mod in these questions please tell

You have to split up the given limits of integration into smaller limits where the function can be negative and positive.

for this mainly for \textit {trigo,or known function} draw graph see which graph is up in intervals

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Question no 54 i am not able to find any substitution possible in this

its putnam beutiful problem
\textbf{dalzells integral} hari shankar sir and jagdish sir solved it before

i know one shorcut using complex number but gives only {\pi} part only

Thanks for referring