Working with constant of integration

First of all, I am a new user, so please bear with what might be a simple question.

If I wanted to solve for y(x) in the following situation: y '(x) = x y(0) = 1 I understand how to set up the integral and assign the answer to y(x)

y(x):= indefinte integral x dx + c (with the +c outside of the integral)

And I can type in

y(0)= 1 Solve--> to find c. (bold equal sign)

Now, how do I put the c back into y(x) so that y(x) would then symbolically evaluate to x^2 + 1?

Of course, this is simple enough to do by hand. I'm asking for the steps so I can use them in more complicated problems.

Phil

P.S. I don't want to use PDSolve as this would be used in teaching a DE class.