I only have time to get you started tonight.

The idea is to consider a small element ds of the total length of wire S.

This is connected angle φ at P between the perpendicular to P and ds as shown, with the zero at the perpendicular.

This is geometry.

Use the formula given to calculate the flux at P due to ds and integrate from φ = 0 to φ= (90 - θ2).

This gives the part of the flux generated on the right hand side of the perpendicular.

Do the same on the left hand side using φ = 0 to (θ1-90) as the limit.

So you change the variable from dB to ds and finally dφ using the formula given and the geometry.

Add the two contributions together.