Integral calculus is easy - it's all about calculation. Where math got hard for me was when the focus shifted from calculation to proof (abstract algebra, number theory, real analysis). I thought I could coast by with the same sort of intuitive understanding I had with calculus, but I was wrong and I didn't have the self discipline that was required to do well.
With proof you have to do a whole host of them first. I remember, filling a book with proof. Eventually, a pattern will emerge and they would be easy. At first, I used to hate them but practise enough times and you would want them to show on the exams.
For me it was quite the opposite. I didn't begin to show any particular interest in mathematics until proof based courses came into the picture. I would certainly not have earned a degree in mathematics were it not for my interests being piqued by a capricious used bookstore purchase of E. Kampke's Set Theory when just out of high school. It was the axiomatic proof based method that appealed to me. Calculation, on the other hand, seemed to my naive 17-year-old self to be terribly banal.
To put things in perspective, and to possibly invalidate the general application of my insight on the matter, Calculus was in fact the only course I passed my final semester of high school. I received a D shortly before I dropped out altogether. The D score was earned only after being the only student to ace the final, a task which was itself only possible after I proved the first fundamental theorem to myself (thanks to an especially verbose description of it in one of the exam questions) during the course of the test.
To this day I find that the actual solving of equations to be tedious and can only be interested in problems tenable to axiomatic and algorithmic approaches. Thats where all the fun is imho. Who cares about actually determining a number (or equation)? [the answer: all the smartest people do.]