How to do this definite integral

Question

₀∫⁴ sqrt(2x+1)dx 

 

In my book in the solutions section, the upper and lower limit seem to have changed but Im not sure how they got there and how to do it. 

Answer 1

SUBSTITUTION!

Let u = 2x+1; then du = 2 dx, so dx = ½(du) and the integrand is rewritten as u^½.

 

That is easy to antidifferentiate. If you evaluate this u-version, then you have to substitute 0 & 4 into the u formula, thus the new limits are a=1, b=9.