What are the prerequisite skills needed to solve calculus problems?

Everything up to pre-calculus is needed to solve calculus problems, assuming trigonometry is part of pre-calculus.  In some school, i think they make precalc and trig separate, but otherwise, once you've finished precalculus, you have all the tools necessary to learn calculus.

Calculus is a little more conceptual than the math you've learned in previous years, but usually when solving math problems(calculus problems included), the final steps will almost always include some algebra skills that you are supposed to know, i.e. something like factoring polynomials.

As for the history of calculus, i personally think that's a good topic to investigate. Wikipedia should do the job in your research.

Algebra manipulation
Cartesian plane
Trig identities and funtions
Infinite series
Area of trapezoid

stuff like this... these things that you have been taught  

But I am sorry that you find it so boring...

I am a math major I find art to be pompous and over inflated especially modern art...