Edited to add: I see a lot of people commenting on how 1 C isn't bad, it won't affect much, get past it (I'm paraphrasing). At this stage in most young people's life, they are still learning on how to identify "self". People get pegged as the one good at sports, good at art, etc. And for some, they are good at learning/test taking/etc. & are known for getting good grades - it becomes a part of who they are, especially if they have done well throughout most of their school years. Some of them work very hard for those grades, others it comes easily, but it is still a defining aspect of them at this stage. As a result it can be very difficult to not achieve what you have always had in the past.
In my undergraduate work prior to pharmacy school, most of my classes were curved to accommodate the difficulty of the material & the diversity of the students enrolled. In pharmacy school, the work is hard, there is not a curve in most classes, & -everyone- is the "smartest" in their class. It was a hard adjustment to accept B's (& sometimes lower) as the very best I could do, & being OK with that.
So I just want to acknowledge to the original poster, A., that you are more than the grades you receive on paper. You are all of the knowledge that went into getting those grades, all the hard work that went into learning that knowledge, and all the maturity you gain when you realize you maybe didn't put forth your best effort. :)
Original response: Everyone has experiences like this (maybe not college, but a life-changing "wake-up" experience in some area as they mature), and it is really hard to accept at first. We try our best, make assumptions, and then fall flat, and it bruises our ego, makes us feel like we failed, and embarrasses us to acknowledge.
The best thing you can do about it is to take it as a learning experience. Be up-front with your uncle, the same way you did in your post. Acknowledge that you mis-read the syllabus, and went into the class with lower expectations than you should have. Let him know that you realize that every learning opportunity deserves respect, & you will be making sure to approach all of your classes in the future with the same determination, regardless of how many credits they are.
I'm not sure what your other classes are, but I know calculus is a difficult class, especially at the college level. So you must be doing something right to be getting good grades in your other classes, as well as taking difficult subjects! Focus on the positive, & let this experience change you for the better. One credit will most likely not have a significant impact on your GPA overall, but you can talk with your class advisor to make sure you are taking an appropriate class load for future semesters so that you can continue to excel.
Best of luck, I know first-hand how challenging college can be! T. :)