// this is how the graphical object of the pictureBox1 control is declared

public static Graphics g;

private void Form1_Load(object sender, EventArgs e)
{

    g = pictureBox1.CreateGraphics();

}

// this is how I save what was drawn on g

private Bitmap DrawControlToBitmap(Control control)

{

    Bitmap bitmap = new Bitmap(control.Width, control.Height);

    Graphics graphics = Graphics.FromImage(bitmap);

    Rectangle rect = control.RectangleToScreen(control.ClientRectangle);

    graphics.CopyFromScreen(rect.Location, Point.Empty, control.Size);

    return bitmap;

}

private void SaveToolStripMenuItem_Click(object sender, EventArgs e)

{

    Bitmap bitmap = DrawControlToBitmap(pictureBox1);

    SaveFileDialog dialog = new SaveFileDialog();

    dialog.Filter = "PNG File (*.png)|*.png|JPEG File (*.jpeg)|*.jpeg|ICON File (*.ico)|*.ico|BITMAP File (*.bmp)|*.bmp|ALL FILES (*.*)|*.*";

    if (dialog.ShowDialog() == DialogResult.OK)
    {

        if (dialog.FilterIndex == 1)
        {
            bitmap.Save(dialog.FileName, System.Drawing.Imaging.ImageFormat.Png);
        }

        else if (dialog.FilterIndex == 2)
        {
            bitmap.Save(dialog.FileName, System.Drawing.Imaging.ImageFormat.Jpeg);
        }

        else if (dialog.FilterIndex == 3)
        {
            bitmap.Save(dialog.FileName, System.Drawing.Imaging.ImageFormat.Icon);
        }

        else if (dialog.FilterIndex == 4)
        {
            bitmap.Save(dialog.FileName, System.Drawing.Imaging.ImageFormat.Bmp);
        }

        else if (dialog.FilterIndex == 5)
        {
            bitmap.Save(dialog.FileName, System.Drawing.Imaging.ImageFormat.Bmp);
        }

    }
}