Definitely (B-A)/N-> H and NOT (2N) as the Casio will try to multiply N*2 (doesn't support 2 variable names, and this could also be your problem further down in your program as well.)
You should check to see if your CASIO has other looping structures other than GOTO (although I am a down and dirty programmer and don't have any aversion to this). ie Do Loops or IF, THEN, ELSE to do the summation under the function. Certain words are reserved as programming commands, but your use of 2Hf and 2HL may not be allowed by the CASIO (they could be, check your manual if your calculator allows long variable names). On a Ti 83/84 this would not be an allowed variable name, but would be interpreted as 2*H*f or 2*H*L.
You might also do a web search or visit a Casio programming site and see if someone has done this for you (I suspect they have). This is an integration function as you have named it and new calculators have this function built in. However, 20 years ago, this wasn't the case and older programmable calculators had to use this type of program to compensate for not having built in numerical integration. You should be successful in finding a BASIC program and making it would with your CASIO as it is fairly similar.