Evaluate the integral using integration by parts?

[turbokaz]

Homework Statement

Evaluate the integral.
Integral = x f(x) dx from 0 to 1 when f(1) = 6, f'(1) = 7.
Answer choices:
A. 11/6 + 1/6 integral from 0 to 1 x^3f''(x)dx
B. 11/12 - 1/6 integral from 0 to 1 x^3f''(x)dx
C. 11/3 + 1/2 integral from 0 to 1 x^2f'(x)dx
D. 11/3 - 1/2 integral from 0 to 1 x^2f'(x)dx
E. 11/4 - 1/2 integral from 0 to 1 x^2f"(x)dx

Homework Equations

The Attempt at a Solution

So just by looking at the answer choices, the method is integration by parts. Based on what was given, I determined that f(x)=x^2+5x. But that would give an integral of x(x^2+5x), which doesn't even need integration by parts to solve. I am stuck here and don't know how the answer choices are gotten.

 

[vela]

Did you try integrating by parts?