Calculus task

Hello, I'm looking for someone to help me with this equation: f(x)= (sign(a*x) * (EXP( a * ABS(x) )-1) * (EXP( b*(x^2) + c*x )) x between -1 and 1 a is a sensitivity parameter, large negative values of a -> steep function shape, large positive a -> emphasize large values of x b is negative, large b lowers weight on extreme values of x c is location parameter if a=0 and b=0 and c=0 then y=x I would need to make this function behave more nicely - normalize with it's integral or something like that. The task is to improve the function, so that the definite integral of abs(f(x)) between -1 to 1 is constant, given any values a, b, c. If this is not possible, is it possible to find the maximum? You can also suggest some other approach, but the parameters should work in a similar way. Thanks!