Estimate $I=\int_{1}^{7}\left(3 x^{2}+2 x+5\right) d x$ using a Riemann sum, $n=3$ subintervals, and
(a) Left endpoints.
\[
I \approx
\]
(b) Right endpoints.
\[
I \approx 1
\]

Step 1 ：First, we need to find the width of each subinterval. The interval from 1 to 7 is of length 6, so each of the 3 subintervals will be of width 2. The left endpoints of these subintervals are 1, 3, and 5.

Step 2 ：Next, we evaluate the function at these points and multiply by the width of the subintervals: \(I \approx 2[(3(1)^2 + 2(1) + 5) + (3(3)^2 + 2(3) + 5) + (3(5)^2 + 2(5) + 5)]\)

Step 3 ：Simplify the above expression: \(I \approx 2[10 + 38 + 90]\)

Step 4 ：Further simplify: \(I \approx 2[138]\)

Step 5 ：\(\boxed{I \approx 276}\) is the estimate for the integral using left endpoints.

Step 6 ：The right endpoints of the subintervals are 3, 5, and 7.

Step 7 ：We evaluate the function at these points and multiply by the width of the subintervals: \(I \approx 2[(3(3)^2 + 2(3) + 5) + (3(5)^2 + 2(5) + 5) + (3(7)^2 + 2(7) + 5)]\)

Step 8 ：Simplify the above expression: \(I \approx 2[38 + 90 + 162]\)

Step 9 ：Further simplify: \(I \approx 2[290]\)

Step 10 ：\(\boxed{I \approx 580}\) is the estimate for the integral using right endpoints.