What happens to the accuracy of the area estimation under a curve when the number of rectangles in a Riemann sum is increased?

Evaluate the integral ∫ from 0 to 2 of (3x^2 + 4) dx using the sum and constant multiple rules.

Compute ${\int }_{-3}^2\frac{dx}{\sqrt{7-x}}$.

Compute the integral: ${\int }_0^{\frac{\pi }{2}}{\sin }^{6}xdx$.

Evaluate the definite integral ${\int }_{-2}^2\sqrt{4+x^2}\sin xdx$.