in programming, integrals are calculated using the rough form of an integral. that is, the solution to an integral is the sum of f(x) dx. typically, you evaluate the function at x in a DO/WHILE/FOR loop in a function or subroutine and pass the value back to main to add to the previous delta value. since integrals are done over a range (or ranges, with double integrals), you just create a loop with the appropriate beginning and ending indices or the appropriate number of iterations and you only have to figure out how to code the equation once.
programming in such a way is often done concurrently with studying beginning calculus. really once you understand limits, sums, and series, you're pretty much good to go. But you have to understand them first to know what they're telling you and, ultimately, what you're looking for.
I can't speak for game programming exactly, since you can really arbitrarily define rules in any game world, but games are looking more and more like technical simulations with the incorporation of PhysX and Havok, and the more something in a 3D game responds the way you would expect it to in real life (like the trajectory of a bullet, including gravitational, wind effects, deceleration, elapsed time, etc.), the deeper the immersion. For that you need not just math, but physics with advanced math.
for the record, fortran is much better for number crunching than C/C++. and use of float variables, even double precision ones, is not strange.