Evaluate the definite integral \[\int_{-1}^2 (x+1)^2 \,dx .\]

Find the value of the constant \(a\) so that \[\int_{-1}^2 a(x+1)^2 \,dx = 1 .\]

Sketch graphs to illustrate how these definite integrals are related.

Evaluate the definite integral \[\int_{-1}^2 (x+1)^2 \,dx .\]

Find the value of the constant \(a\) so that \[\int_{-1}^2 a(x+1)^2 \,dx = 1 .\]

Sketch graphs to illustrate how these definite integrals are related.