Assume there is an Ideal Random Number Generator which generates any real number between 0 and given integer. Two numbers are generated from the above generator using integer A and B, let's assume the numbers generated are X1 and X2. There is another integer C. What is the probability that summation of X1 and X2 is less than C.
Draw the sample space on axes $X_1, X_2$. You should get a rectangle of area $AB$. Now shade the portion $X_1 + X_2 < C$ in this rectangle.
Now consider cases where $C \in \,$ one of the following intervals $(0 < \min(A, B)), [\min(A, B), \max(A, B)], (\max(A, B), A+B), (A+B, \infty)$...