We like to do easy parts first. The integrand, right of equality (Fthrust - Fpropeller) was zero before change started, when time was t < 0+. We suppose the firing happens very fast so that either "dt" is zero or (Fthrust - Fpropeller) remains what it was at the start ~ zero. Use either approximation to set "right of equality" equal to zero for the event. Left of equality integrates immediately.