I am asked to calculate this integral $\int_{-1}^{5}(1+3x)dx$ using the Riemann sum definition with $\Delta x = \Delta x_{i} = \frac{b\ - \ a}{n}$ (as in all the intervals in the x axis are evenly spaced) and using the midpoint of each $\Delta x_{i}$, as in $c_{i} = \frac{1}{2}(x_{i} + x_{i + 1}) \ (i=1,2,3, \cdots, n - 1). $
Is it right to say that $c_{i}$ will be equal to $\frac{i\Delta x + a + i\Delta x + a + \Delta x}{2}$, with $x_{i} = i\Delta x + a $ and $x_{i+1} = i\Delta x + a + \Delta x$? Because that's where I think I'm making a mistake.
Thanks in advance.