True/False

Please shop solution/explanation.

(a)_____ⁿ_i=1 i =n(n+1)/2.

(b)_____ ⁵₁ f(x)dx = -¹₅ f(x)dxby definition.

(c)_____¹_-1xdx = 0

(d)____ ¹⁰_-1 1/x dxcan be estimated by using a Riemann sum.

(e)_____Riemann sum method is applicable only when the function is positive.

(f)_____ A definite integral exists as long as it is continuous, and bounded over the interval of interest

(g)_____ ^b_a {area above x axis between a and b} - {area below x axis between a and b}.

(h)_____ Following the Antiderivative and Definite Integrals conjecture in

Sect 4.4, we have ¹_-1 1/x² dx =-2because 1/dx(1/x)= -1/x².

(i)_____ For any integrable function f, ^c_a f(x)dx = ^b_a f(x)dx + ^c_b f(x)dx, where a

(j)_____^x₁ f(t)dt is a function of x, where x is a variable (i.e., not a fixed constant).